(1+(2^(2))/(2)+(2^(4))/(23)+(2^(6))/(24)-cdots)/(1+(1)/(2)+(2)/(13)+(2^(2))/(14)+cdots)

If (1)/(1^(2))+(1)/(2^(2))+(1)/(3^(2))+cdots "to" oo = (pi^(2))/(6) then (1)/(1^(2)) +(1)/(3^(2))+(1)/(5^(2))+cdots equals

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

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)) .

If S_(1), S_(2),cdots S_(n) , ., are the sums of infinite geometric series whose first terms are 1, 2, 3,…… ,n and common ratios are (1)/(2) ,(1)/(3),(1)/(4),cdots,(1)/(n+1) then S_(1)+S_(2)+S_(3)+cdots+S_(n) =

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

Find the 24^(th) term of the H.P (2)/(7),(1)/(5),(2)/(13),(1)/(8), cdots

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)) =

Prove that, tan^(2) (pi/6) cdot tan^(2)(2pi/16) cdot tan^(2) (3pi/16) cdot tan^(2) (4pi/16) cdot tan^(2) (5pi/16) cdot tan^(2) (6pi/16) cdot tan^(2)(7pi/16) = 1 .

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

If S = (2^(2)-1)/(2)+(3^(2)-2)/(6)+(4^(2)-3)/(12)+ cdots upto 10 terms then S is equal to