`60^(2)-59^(2)+58^(2)-57^(2)+ cdots +2^(2)-1^(2)` =

Evaluate 50^(2)-49^(2)+48^(2)-47^(2)+ cdots+2^(2)-1^(2) .

8^(2)+9^(2)+10^(2)+ cdots +22^(2) =

11^(2)+12^(2)+13^(2)+ cdots +32^(2) =

lim_(n rarr oo)(n(1^(3)+2^(3)+3^(3)+cdots n^(3))^(2))/((1^(2)+2^(2)+3^(2)+cdots+n^(2))^(3)) =

If x + y + z = xyz, then prove that (2x)/(1- x^(2)) + (2y)/(1 - y^(2)) + (2z)/(1 - z^(2)) = (2x)/(1 - x^(2))cdot (2y)/(1 - y^(2))cdot (2z)/( 1- z^(2)) .

Find the sum 1^(2) + (1^(2)+2^(2))+ (1^(2)+2^(2)+3^(2))+ cdots up to 22 nd term.

If x=sec57^(@) , then cot^(2)33^(@)+sin^(2)57^(@)+sin^(2)33^(@)+cosec^(2)57^(@)cos^(2)33^(@)+sec^(2)33^(@)sin^(2)57^(@) is equal to:

Evaluate: (sec^(2)(90^(@) - theta)-cot^(2) theta)/(2 (sin^(2) 25^(@)+sin^(2) 65^(@)))+(2 sin^(2)30^(@)tan^(2) 32^(@) tan^(2)58^(@))/(3(sec^(2)33^(@)-cot^(2)57^(@))) .

Prove that (sin^(2)30^(@)+cos^(2)30^(@))/(sec^(2)57^(@)-tan^(2)57^(@))=1

Find the sum to n terms of the series 1^(2)/(1)+(1^(2)+2^(2))/(1+2)+(1^(2)+2^(2)+3^(2))/(1+2+3)+cdots