Question 827159
<pre>
{{{cross((sum(1/r^2,r=1,n))>=2-1/n)}}}

This is not true!

Although equality holds for n=1:

{{{1/1^2}}}{{{""=""}}}{{{1}}}
{{{2-1/1}}}{{{""=""}}}{{{1}}}

It isn't true for n=2 or greater, for when n=2

{{{1/1^2+1/2^2}}}{{{""=""}}}{{{1+1/4}}}{{{""=""}}}{{{1.25}}}
yet
{{{2-1/2}}}{{{""=""}}}{{{1.5}}}, {{{""<=""}}} holds but not {{{"">=""}}}

And when n=3

{{{1/1^2+1/2^2+1/2^3}}}{{{""=""}}}{{{1+1/4+1/8}}}{{{""=""}}}{{{1.375}}}
yet
{{{2-1/3}}}{{{""=""}}}{{{1.666667}}}, again {{{""<=""}}} holds but not {{{"">=""}}}.

Euler proved in 1735 that the the sum on the left approaches the irrational
number {{{pi^2/6}}} = 1.6449340668482264... and it is an increasing function, so it
is always less that {{{pi^2/6}}}.

The expression on the right is also increasing, and approaches 2.  But
beginning with the third term it is already larger than the left side can 
ever be!

Edwin</pre>