SOLUTION: 1+(1/4)+(1/9)+(1/25)+........=?

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Question 1061950: 1+(1/4)+(1/9)+(1/25)+........=?
Found 3 solutions by rothauserc, math_helper, ikleyn:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website!
1+(1/4)+(1/9)+(1/25)+........= ?
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This summation is know to converge to (pi^2)/ 6 = 1.644934
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The summation can be written
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summation from k = 1,2,...,m of 1 / k^2
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One proof involves using De Moivre's formula and the identities for cotangent and cosecant functions.
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Another proof uses Fourier series
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Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website!
This series is known as Euler's Series. The solution is not trivial and fairly lengthy regardless of approach. Here is a paper where the author discusses six different solutions, each using a different approach. A few justifications are missing here and there but in the end, they all reach the correct result.
https://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/07468342.di020759.02p00026.pdf

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.
1+(1/4)+(1/9)++(1/25)+........=?
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Do you know that you submitted your series with a mistake?

You missed the term +(1/16), which I highlighted in my response.