The sum of the infinite series, 1/2^2 - 2/3^2 + 3/4^2 - 4/5^2 + ... is given as pi^2/12 - log 2 on pages 64-65 in the book "Summation of Series" by L. B. W. Jolley, 2nd ed., 1961, Dover Pubs. Inc. (the ^ symbol denotes exponentiation in the above series and sum).
For most of the series in his book, he lists a source (reference), but does not do so for this one.
My question is: Who proved this originally and where and when was it first published? I would like to see a proof for this, especially the original one (in English), but I will be satisfied with any proof you can provide. However, I would also like to know who first proved it and when, along with a reference to where it was published.
Actually, the infinite series you want to discuss in this posting is not a special sequence. It is a combination of two famous sequences and those two famous ...
Solution Summary
This explains the result of a given sum of an infinite series. The proof of a sum for given infinite series of constants are determined. A closed form analysis is provided.
... you find a specific geometric series that sums to -30 ? Solution If we take a = -2, common multiple r =2 and n = 4 terms then sum. And for infinite series put a ...
...Series and infinite series are examined ... Terms in a convergent series may be rearranged without changing the sum. However, the terms of a divergent series may be ...
... that finding the finite formula for the infinite sum 1+1 ... Euler finally showed in 1741 that this sum converges to ... 2) Recall that the Maclaurin series for sin??(x ...
... 2. Determine whether the given infinite series converges or ... If it converges, find its sum ... ... Convergence, Divergence and sums of Infinite Sequences are ...
Infinite Geometric Series: Square Inscribed in Circle Radius. A square is inscribed in a circle of radius 100. ... What is the sum of all of the shaded areas? ...
... a) The summation becomes E(X) = sum c^k * p(x) = sum (c/2)^k = c/2 + (c/2)^2 + (c/2)^3 + ... This is an infinite geometric series with common ratio c/2. Read ...
Infinite Series of Real Numbers (Cesaro summable ... Separate the terms into two sums - those with a coefficient of 1 and the others (line 5). Rewrite as summation ...
... 2 rad can be represented by the infinite series S = sum... 2n+1)!] Let its partial sum be SN = sum (0 to ... Use the Ratio test to show the series converges absolutely ...
