Mixing
$ C _ { 1 } - frac { 1 } { 2 } C _ { 2 } + frac { 1 } { 3 } C _ { 3 } + ldots + ( - 1 ) ^ { n - 1 } frac { 1...
-4
$begingroup$
show that $$C _ { 1 } - frac { 1 } { 2 } C _ { 2 } + frac { 1 } { 3 } C _ { 3 } + ldots ldots ldots + ( - 1 ) ^ { n - 1 } frac { 1 } { n } C _ { n } = 1 + frac { 1 } { 2 } + frac { 1 } { 3 } + ldots ldots + frac { 1 } { n }$$
Here $$C_{k} = n!/k!(n-k)!$$
permutations binomial-theorem
asked Jan 10 at 9:06
Ravi AgarwalRavi Agarwal
13
$endgroup$
add a comment |
-4
$begingroup$
show that $$C _ { 1 } - frac { 1 } { 2 } C _ { 2 } + frac { 1 } { 3 } C _ { 3 } + ldots ldots ldots + ( - 1 ) ^ { n - 1 } frac { 1 } { n } C _ { n } = 1 + frac { 1 } { 2 } + frac { 1 } { 3 } + ldots ldots + frac { 1 } { n }$$
Here $$C_{k} = n!/k!(n-k)!$$
permutations binomial-theorem
asked Jan 10 at 9:06
Ravi AgarwalRavi Agarwal
13
$endgroup$
$begingroup$
Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
$endgroup$
– Martin R
Jan 10 at 9:13
3
$begingroup$
What is $C_k$ here?
$endgroup$
– J.G.
Jan 10 at 9:25
$begingroup$
I agree with J.G. and would like to know what $C_1,C_2,C_3,$ etc. are, as a formula in terms of $k$ for $C_k.$ IMO there are likely many series of numbers denoted like that,
$endgroup$
– coffeemath
Jan 10 at 10:27
$begingroup$
math.stackexchange.com/questions/437523/…
$endgroup$
– lab bhattacharjee
Jan 10 at 12:31
$begingroup$
i have edited this please help
$endgroup$
– Ravi Agarwal
Jan 10 at 13:14
add a comment |
-4
-4
-4
1
$begingroup$
show that $$C _ { 1 } - frac { 1 } { 2 } C _ { 2 } + frac { 1 } { 3 } C _ { 3 } + ldots ldots ldots + ( - 1 ) ^ { n - 1 } frac { 1 } { n } C _ { n } = 1 + frac { 1 } { 2 } + frac { 1 } { 3 } + ldots ldots + frac { 1 } { n }$$
Here $$C_{k} = n!/k!(n-k)!$$
permutations binomial-theorem
asked Jan 10 at 9:06
Ravi AgarwalRavi Agarwal
13
$endgroup$
show that $$C _ { 1 } - frac { 1 } { 2 } C _ { 2 } + frac { 1 } { 3 } C _ { 3 } + ldots ldots ldots + ( - 1 ) ^ { n - 1 } frac { 1 } { n } C _ { n } = 1 + frac { 1 } { 2 } + frac { 1 } { 3 } + ldots ldots + frac { 1 } { n }$$
Here $$C_{k} = n!/k!(n-k)!$$
permutations binomial-theorem
permutations binomial-theorem
asked Jan 10 at 9:06
Ravi AgarwalRavi Agarwal
13
asked Jan 10 at 9:06
Ravi AgarwalRavi Agarwal
13
edited Jan 10 at 13:13
Ravi Agarwal
asked Jan 10 at 9:06
Ravi AgarwalRavi Agarwal
13
asked Jan 10 at 9:06
Ravi AgarwalRavi Agarwal
13
asked Jan 10 at 9:06
Ravi AgarwalRavi Agarwal
13
13
$begingroup$
Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
$endgroup$
– Martin R
Jan 10 at 9:13
3
$begingroup$
What is $C_k$ here?
$endgroup$
– J.G.
Jan 10 at 9:25
$begingroup$
I agree with J.G. and would like to know what $C_1,C_2,C_3,$ etc. are, as a formula in terms of $k$ for $C_k.$ IMO there are likely many series of numbers denoted like that,
$endgroup$
– coffeemath
Jan 10 at 10:27
$begingroup$
math.stackexchange.com/questions/437523/…
$endgroup$
– lab bhattacharjee
Jan 10 at 12:31
$begingroup$
i have edited this please help
$endgroup$
– Ravi Agarwal
Jan 10 at 13:14
add a comment |
$begingroup$
Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
$endgroup$
– Martin R
Jan 10 at 9:13
3
$begingroup$
What is $C_k$ here?
$endgroup$
– J.G.
Jan 10 at 9:25
$begingroup$
I agree with J.G. and would like to know what $C_1,C_2,C_3,$ etc. are, as a formula in terms of $k$ for $C_k.$ IMO there are likely many series of numbers denoted like that,
$endgroup$
– coffeemath
Jan 10 at 10:27
$begingroup$
math.stackexchange.com/questions/437523/…
$endgroup$
– lab bhattacharjee
Jan 10 at 12:31
$begingroup$
i have edited this please help
$endgroup$
– Ravi Agarwal
Jan 10 at 13:14
$begingroup$
Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
$endgroup$
– Martin R
Jan 10 at 9:13
$begingroup$
Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
$endgroup$
– Martin R
Jan 10 at 9:13
3
3
$begingroup$
What is $C_k$ here?
$endgroup$
– J.G.
Jan 10 at 9:25
$begingroup$
What is $C_k$ here?
$endgroup$
– J.G.
Jan 10 at 9:25
$begingroup$
I agree with J.G. and would like to know what $C_1,C_2,C_3,$ etc. are, as a formula in terms of $k$ for $C_k.$ IMO there are likely many series of numbers denoted like that,
$endgroup$
– coffeemath
Jan 10 at 10:27
$begingroup$
I agree with J.G. and would like to know what $C_1,C_2,C_3,$ etc. are, as a formula in terms of $k$ for $C_k.$ IMO there are likely many series of numbers denoted like that,
$endgroup$
– coffeemath
Jan 10 at 10:27
$begingroup$
math.stackexchange.com/questions/437523/…
$endgroup$
– lab bhattacharjee
Jan 10 at 12:31
$begingroup$
math.stackexchange.com/questions/437523/…
$endgroup$
– lab bhattacharjee
Jan 10 at 12:31
$begingroup$
i have edited this please help
$endgroup$
– Ravi Agarwal
Jan 10 at 13:14
$begingroup$
i have edited this please help
$endgroup$
– Ravi Agarwal
Jan 10 at 13:14
add a comment |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3068412%2fc-1-frac-1-2-c-2-frac-1-3-c-3-ldots%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
draft saved
draft discarded
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
draft saved
draft discarded
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3068412%2fc-1-frac-1-2-c-2-frac-1-3-c-3-ldots%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be put on hold. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers.
$endgroup$
– Martin R
Jan 10 at 9:13
3
$begingroup$
What is $C_k$ here?
$endgroup$
– J.G.
Jan 10 at 9:25
$begingroup$
I agree with J.G. and would like to know what $C_1,C_2,C_3,$ etc. are, as a formula in terms of $k$ for $C_k.$ IMO there are likely many series of numbers denoted like that,
$endgroup$
– coffeemath
Jan 10 at 10:27
$begingroup$
math.stackexchange.com/questions/437523/…
$endgroup$
– lab bhattacharjee
Jan 10 at 12:31
$begingroup$
i have edited this please help
$endgroup$
– Ravi Agarwal
Jan 10 at 13:14