If `S_n=1+3+6+10+....+(n(n+1))/2` then `S_n` is

If S=sum_(n=1)^(10)(2n+(1)/(2)), then S

If S_(n) denotes the sum of first 'n' natural numbers then s_(1)+S_(2)x+S_(3)x^(2)+.........+S_(n) x^(n-1)+......oo=(1-x)^(-n) then n is

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

if S_n = C_0C_1 + C_1C_2 +...+ C_(n-1)C_n and S_(n+1)/S_n = 15/4 then n is

if S_n = C_0C_1 + C_1C_2 +...+ C_(n-1)C_n and S_(n+1)/S_n = 15/4 then n is

(1) .Let S_n denote the sum of the first 'n' terms and S_(2n)= 3S_n. Then, the ratio S_(3n):S_n is: (2) let S_1(n) be the sum of the first n terms arithmetic progression 8, 12, 16,..... and S_2(n) be the sum of the first n terms of arithmatic progression 17, 19, 21,....... if S_1(n)=S_2(n) then this common sum is

If S_(n) = sum_(n=1)^(n) (2n + 1)/(n^(4) + 2n^(3) + n^(2)) then S_(10) is less then

If S_(n) = sum_(n=1)^(n) (2n + 1)/(n^(4) + 2n^(3) + n^(2)) then S_(10) is less then

In a series, if t_n = (n^(2) -1)/(n+1) , then S_6 - S_3= _______.