Re: The Sum (r=1 to n) (1/ r^2)
"donkey" <newsdonkey@xxxxxxxxxxx> wrote:
someone tells me there is no elementary expression about this sum "Sum
(r=1 to n) (1/ r^2)", in terms of n. Can any one tells me why? thanks
in advance.
Others have mentioned that it can be expressed exactly in terms of various
non-elementary functions. BTW, yet another such function is the Hurwitz
zeta function.
Your sum can also be approximated rather easily. For example, the simple
expression
Pi^2/6 - 1/(n - 1 + 1/(Pi^2/6 - 1))
overestimates your sum, with error < 0.003 .
David
.
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