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April 4th, 2018, 10:21 AM   #1
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Infinite convergent series.

How do I find the limiting value of any convergent series ?
I mean, how do I approach it? ("steps", maybe?)

ex : (1^-2)+(2^-2)+(3^-2)+.... = pi^2/6

I know the solution of this problem but how on earth did anyone (Euler) come up with this ?
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( I'm trying to solve this
(1^-3)+(2^-3)+(3^-3)+..... = ? )
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April 4th, 2018, 10:30 AM   #2
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How Euler found the sum of inverse squares

I don't believe there is a general strategy to your problem.

You can try to match up the coefficients with a Taylor series.

A handful of series, such as the geometric series, have known results.
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April 4th, 2018, 10:45 AM   #3
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April 4th, 2018, 01:40 PM   #4
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That was awesome. Thanks to romsek and v8archie for posting them.

-Dan
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April 4th, 2018, 03:35 PM   #5
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Just remembered this mildly awesome one too, although it has less to do with Euler.

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