[tex] \frac{1}{ 2^{2} } = \frac{1}{2*2} \ \textless \ \frac{1}{1*2}
[/tex]=[tex] \frac{1}{1} - \frac{1}{2} [/tex]
[tex] \frac{1}{ 3^{2} } = \frac{1}{3*3} \ \textless \ \frac{1}{2*3} = \frac{1}{2} - \frac{1}{3} [/tex]
[tex] \frac{1}{ 4^{2} } = \frac{1}{4*4} \ \textless \ \frac{1}{3*4} = \frac{1}{3} - \frac{1}{4} [/tex]
.
.
[tex] \frac{1}{ 2011^{2} }= \frac{1}{2011*2011} \ \textless \ \frac{1}{2010*2011} = \frac{1}{2010} - \frac{1}{2011} [/tex]
+
[tex] \frac{1}{ 2^{2} } + \frac{1}{ 3^{2} } + \frac{1}{ 4^{2} } +...+ \frac{1}{ 2011^{2} } \ \textless \ \frac{1}{1} - \frac{1}{2011} = \frac{2011-1}{2011} = \frac{2010}{2011} [/tex]
