1^(2)+4^(2)+7^(2)+10^(2)+cdots+h_(n)

Find the sum to n terms of the series 3//(1^(2) xx2^(2))+5//(2^(2)xx3^(2))+7//(3^(2)xx4^(2))+ 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)) =

Find the sum of n terms of the series 1 + 4/5 + 7//5^(2) + 10//5^(3)+ cdots

If a , a_(1) , a_(2) ,a_(3) , cdots a_(2n), b are in A.P. and a, g_(1) , g_(2) , g_(3) , cdots , g_(2n), b are in G.P. and h is the H.M of a and b then prove that (a_(1)+a_(2n))/(g_(1)g_(2n))+(a_(2)+a_(2n-1))/(g_(2)g_(2n-1))+cdots+ (a_(n)+a_(n+1))/(g_(n)g_(n+1))=(2n)/(h)

Let a = 111 cdots 1 (55 digits ) , b=1 + 10 + 10^(2)+ cdots+ 10^(4) c= 1+10^(5) +10^(10)+ 10^(15) + cdots+ 10^(50) then

If H_(n) =1+(1)/(2)+ cdots + (1)/(n) then value of S_(n) =1 + (3)/(2) + (5)/(3) +cdots + (2n-1)/(n) is

Find the sum 1+(1)/(1+2) + (1)/(1+2+3) + cdots+ (1)/(1+2+3+cdots+ n )

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) =

The sum to n terms of the series 1+2 (1+(1)/(n))+3 (1+(1)/(n))^(2)+ cdots is given by

Find the sum of the series 1.n + 2 .(n-1) + 3.(n-2) + cdots + ( n-1) .2 + n.1.