If `S_n=1+2+3+.......n, n in N`, then `32+34+ 36+.......+74=`

Let S_n, be the sum of n terms of 40, 38, 36, 34 ......., then S_n, can be: (A) 310 (B) 180 (C) 330 (D) -42

In an A.P. if a=2, t_(n)=34 ,S_(n) =90 , then n=

In an A.P. if a=2, t_(n)=34 ,S_(n) =90 , then n=

Prove the following by the method of induction for all n in N : 1.2 + 2.3 + 3.4 +...+ n(n + 1) = n/3 (n+1)(n+2).

S_(n) = (1+2+3+....+n)/( n) then S_(1)^(2) + S_(2)^(2) + S_(3)^(2) + ..... + S_(n)^(2) =

If S_1,S_2,S_3,...,S_n be the sums of first n terms of n G.P.'s whose first terms are each unity and the common ratios are 1, 2, 3,.....,n respectively, prove that S_1+S_2+2S_3+3S_4+.........+(n-1)S_n=1^n+2^n+3^n+....+n^n.

Let S_n=1/1^2 + 1/2^2 + 1/3^2 +….. + 1/n^2 and T_n=2 -1/n , then :

Let S_n=1/1^2 + 1/2^2 + 1/3^2 +….. + 1/n^2 and T_n=2 -1/n , then :

Find S_n for the series. 1.2 + 2.3 + 3.4 +…