Mixing
Basic equation simplification of power series
$begingroup$
Is $$(x^1+x^2+x^3...)^5$$ equal to $$x^5(1+x+x^2+...)^5$$
If so, how? can someone tell me the steps involved in taking the x out? The expression is raised to a power, so how can one simply take x out without expanding? Maybe it is something basic but I don't know how it is done? Thanks in advance.
sequences-and-series discrete-mathematics power-series
edited Jan 26 at 22:18
Maria Mazur
48.2k1260122
asked Jan 26 at 21:34
TeerexTeerex
394
$endgroup$
add a comment |
$begingroup$
Is $$(x^1+x^2+x^3...)^5$$ equal to $$x^5(1+x+x^2+...)^5$$
If so, how? can someone tell me the steps involved in taking the x out? The expression is raised to a power, so how can one simply take x out without expanding? Maybe it is something basic but I don't know how it is done? Thanks in advance.
sequences-and-series discrete-mathematics power-series
edited Jan 26 at 22:18
Maria Mazur
48.2k1260122
asked Jan 26 at 21:34
TeerexTeerex
394
$endgroup$
add a comment |
$begingroup$
Is $$(x^1+x^2+x^3...)^5$$ equal to $$x^5(1+x+x^2+...)^5$$
If so, how? can someone tell me the steps involved in taking the x out? The expression is raised to a power, so how can one simply take x out without expanding? Maybe it is something basic but I don't know how it is done? Thanks in advance.
sequences-and-series discrete-mathematics power-series
edited Jan 26 at 22:18
Maria Mazur
48.2k1260122
asked Jan 26 at 21:34
TeerexTeerex
394
$endgroup$
Is $$(x^1+x^2+x^3...)^5$$ equal to $$x^5(1+x+x^2+...)^5$$
If so, how? can someone tell me the steps involved in taking the x out? The expression is raised to a power, so how can one simply take x out without expanding? Maybe it is something basic but I don't know how it is done? Thanks in advance.
sequences-and-series discrete-mathematics power-series
sequences-and-series discrete-mathematics power-series
edited Jan 26 at 22:18
Maria Mazur
48.2k1260122
asked Jan 26 at 21:34
TeerexTeerex
394
edited Jan 26 at 22:18
Maria Mazur
48.2k1260122
asked Jan 26 at 21:34
TeerexTeerex
394
edited Jan 26 at 22:18
Maria Mazur
48.2k1260122
edited Jan 26 at 22:18
Maria Mazur
48.2k1260122
edited Jan 26 at 22:18
Maria Mazur
48.2k1260122
48.2k1260122
asked Jan 26 at 21:34
TeerexTeerex
394
asked Jan 26 at 21:34
TeerexTeerex
394
asked Jan 26 at 21:34
TeerexTeerex
394
394
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Use $a^5b^5 =(ab)^5$
Second one is $$x^5(1+x+x^2+...)^5 = Big(x(1+x+x^2+...)Big)^5 = (x+x^2+x^3+...)^5$$
answered Jan 26 at 21:36
Maria MazurMaria Mazur
48.2k1260122
$endgroup$
add a comment |
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
});
}
});
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%2f3088787%2fbasic-equation-simplification-of-power-series%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Use $a^5b^5 =(ab)^5$
Second one is $$x^5(1+x+x^2+...)^5 = Big(x(1+x+x^2+...)Big)^5 = (x+x^2+x^3+...)^5$$
answered Jan 26 at 21:36
Maria MazurMaria Mazur
48.2k1260122
$endgroup$
add a comment |
$begingroup$
Use $a^5b^5 =(ab)^5$
Second one is $$x^5(1+x+x^2+...)^5 = Big(x(1+x+x^2+...)Big)^5 = (x+x^2+x^3+...)^5$$
answered Jan 26 at 21:36
Maria MazurMaria Mazur
48.2k1260122
$endgroup$
add a comment |
$begingroup$
Use $a^5b^5 =(ab)^5$
Second one is $$x^5(1+x+x^2+...)^5 = Big(x(1+x+x^2+...)Big)^5 = (x+x^2+x^3+...)^5$$
answered Jan 26 at 21:36
Maria MazurMaria Mazur
48.2k1260122
$endgroup$
Use $a^5b^5 =(ab)^5$
Second one is $$x^5(1+x+x^2+...)^5 = Big(x(1+x+x^2+...)Big)^5 = (x+x^2+x^3+...)^5$$
answered Jan 26 at 21:36
Maria MazurMaria Mazur
48.2k1260122
answered Jan 26 at 21:36
Maria MazurMaria Mazur
48.2k1260122
answered Jan 26 at 21:36
Maria MazurMaria Mazur
48.2k1260122
answered Jan 26 at 21:36
Maria MazurMaria Mazur
48.2k1260122
48.2k1260122
add a comment |
add a comment |
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.
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%2f3088787%2fbasic-equation-simplification-of-power-series%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
