Question

Demonstrati ca:
1/2^2+1/3^2+......+1/2011^2<2010/2011

Answer 1

1/2^2 <1/1*2
1/3^2 <1/2*3
.....................
1/2011^2<1/2010*2011
==================
1/2^2+...+1/2^2011 <1/1*2+1/2*3+...+1/2010*2011<=>
<=>1/2^2+...+1/2^2011<(1/1-1/2) +(1/2 -1/3) +...+(1/2010-1/2011) <=>
<=>1/2^2+...+1/2^2011 <1/1 -1/2011 <=>
<=>1/2^2+...+1/2^2011<2010/2011