My Math Forum Infinite convergent series.

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 April 4th, 2018, 10:21 AM #1 Newbie   Joined: Apr 2018 From: India Posts: 4 Thanks: 0 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 ? . . . . . ( I'm trying to solve this (1^-3)+(2^-3)+(3^-3)+..... = ? )
 April 4th, 2018, 10:30 AM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,297 Thanks: 1221 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. Thanks from greg1313
 April 4th, 2018, 10:45 AM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,598 Thanks: 2583 Math Focus: Mainly analysis and algebra Thanks from greg1313, topsquark and romsek
 April 4th, 2018, 01:40 PM #4 Math Team     Joined: May 2013 From: The Astral plane Posts: 2,035 Thanks: 810 Math Focus: Wibbly wobbly timey-wimey stuff. That was awesome. Thanks to romsek and v8archie for posting them. -Dan Thanks from greg1313
 April 4th, 2018, 03:35 PM #5 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,598 Thanks: 2583 Math Focus: Mainly analysis and algebra Just remembered this mildly awesome one too, although it has less to do with Euler. Thanks from greg1313

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