Mixing
The sum of the given series is?
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$log_42-log_82+log_{16}2-log_{32}2+...$
In the given solution, the answer is given as $1-ln2$. How do I arrive at this solution? Thank you!
logarithms
asked Jan 31 at 18:31
Darshini PoolaDarshini Poola
126
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add a comment |
$begingroup$
$log_42-log_82+log_{16}2-log_{32}2+...$
In the given solution, the answer is given as $1-ln2$. How do I arrive at this solution? Thank you!
logarithms
asked Jan 31 at 18:31
Darshini PoolaDarshini Poola
126
$endgroup$
2
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"However, many sites claim that $1/2−1/3+1/4−1/5ldots$ is an undefined value" -- Out of curiosity, could you please provide reference to at least one such site?
$endgroup$
– zipirovich
Jan 31 at 18:39
add a comment |
$begingroup$
$log_42-log_82+log_{16}2-log_{32}2+...$
In the given solution, the answer is given as $1-ln2$. How do I arrive at this solution? Thank you!
logarithms
asked Jan 31 at 18:31
Darshini PoolaDarshini Poola
126
$endgroup$
$log_42-log_82+log_{16}2-log_{32}2+...$
In the given solution, the answer is given as $1-ln2$. How do I arrive at this solution? Thank you!
logarithms
logarithms
asked Jan 31 at 18:31
Darshini PoolaDarshini Poola
126
asked Jan 31 at 18:31
Darshini PoolaDarshini Poola
126
edited Jan 31 at 18:58
Darshini Poola
asked Jan 31 at 18:31
Darshini PoolaDarshini Poola
126
asked Jan 31 at 18:31
Darshini PoolaDarshini Poola
126
asked Jan 31 at 18:31
Darshini PoolaDarshini Poola
126
126
2
$begingroup$
"However, many sites claim that $1/2−1/3+1/4−1/5ldots$ is an undefined value" -- Out of curiosity, could you please provide reference to at least one such site?
$endgroup$
– zipirovich
Jan 31 at 18:39
add a comment |
2
$begingroup$
"However, many sites claim that $1/2−1/3+1/4−1/5ldots$ is an undefined value" -- Out of curiosity, could you please provide reference to at least one such site?
$endgroup$
– zipirovich
Jan 31 at 18:39
2
2
$begingroup$
"However, many sites claim that $1/2−1/3+1/4−1/5ldots$ is an undefined value" -- Out of curiosity, could you please provide reference to at least one such site?
$endgroup$
– zipirovich
Jan 31 at 18:39
$begingroup$
"However, many sites claim that $1/2−1/3+1/4−1/5ldots$ is an undefined value" -- Out of curiosity, could you please provide reference to at least one such site?
$endgroup$
– zipirovich
Jan 31 at 18:39
add a comment |
1 Answer
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$begingroup$
$ln (1+x) = x - frac{x^2}{2} + frac{x^3}{3} - dots quad $, see series expansion
Put $x = 1 $ and you get the required form
answered Jan 31 at 18:36
ab123ab123
1,799423
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add a comment |
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$begingroup$
$ln (1+x) = x - frac{x^2}{2} + frac{x^3}{3} - dots quad $, see series expansion
Put $x = 1 $ and you get the required form
answered Jan 31 at 18:36
ab123ab123
1,799423
$endgroup$
add a comment |
$begingroup$
$ln (1+x) = x - frac{x^2}{2} + frac{x^3}{3} - dots quad $, see series expansion
Put $x = 1 $ and you get the required form
answered Jan 31 at 18:36
ab123ab123
1,799423
$endgroup$
add a comment |
$begingroup$
$ln (1+x) = x - frac{x^2}{2} + frac{x^3}{3} - dots quad $, see series expansion
Put $x = 1 $ and you get the required form
answered Jan 31 at 18:36
ab123ab123
1,799423
$endgroup$
$ln (1+x) = x - frac{x^2}{2} + frac{x^3}{3} - dots quad $, see series expansion
Put $x = 1 $ and you get the required form
answered Jan 31 at 18:36
ab123ab123
1,799423
answered Jan 31 at 18:36
ab123ab123
1,799423
answered Jan 31 at 18:36
ab123ab123
1,799423
answered Jan 31 at 18:36
ab123ab123
1,799423
1,799423
add a comment |
add a comment |
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$begingroup$
"However, many sites claim that $1/2−1/3+1/4−1/5ldots$ is an undefined value" -- Out of curiosity, could you please provide reference to at least one such site?
$endgroup$
– zipirovich
Jan 31 at 18:39