If-the-zeta-function-of-2-is-2-n-1-1-n-2-2-2-6-the-sum-of-infinite-rational-numbers-why-converges-for-2-6-an-irra

Question Number 9458 by geovane10math last updated on 09/Dec/16

If the zeta function of 2 is

ζ (2) = \underset{n = 1}{\sum^{\infty}} \frac{1}{n^{2}}

ζ (2) = \frac{π^{2}}{6}

the sum of infinite rational numbers,

why converges for \frac{π^{2}}{6}, an irrational

number ?

Commented by geovane10math last updated on 09/Dec/16

K n o w i f a n i n f i n i t e s e r i e d i v e r g e s o r

c o n v e r g e s i s e a s y \dots

H o w c a l c u l a t e t h e v a l u e o f s e r i e ?