This problem is an extension of the well known basel problem and involves finding the sum of
1 + 1/16 + 1/81 ... = 1/1^4 + 1/2^4 + 1/3^4 ... 1/n^4 where n tends to infinity
Euler managed to prove that the sum is finite and converges to pi^4/90. What I do not understand is how he managed to accomplish this.
I have read his proof of the problem involving 2nd powers and fully understand the logic but I fail to see how he manages to extend that to this problem (I have yet to find a complete proof online).
Would somebody please explain the method? Does it involve manipulating the second powers or does it involve some other type of derivation?
Thanks Ahead of Time!