(i)The sum of the first n natural numbers is `[n/3(2n+1)(2n-1),(n^2(n+1)^2)/4,n/6(n+1)(2n+1),(n(n+1))/2]`

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

Find the sum to n terms of the series whose n^(th) term is 2n^3+3n^2-1

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

If the sum of the first n terms of an Arithmetic progression is S_n=nX+1/2n(n-1)Y where X and Y are constants, find S_1 and S_2 .

If the sum of the first n terms of an Arithmetic progression is S_n=nX+1/2n(n-1)Y where X and Y are constants, find The n^th term.

Prove that ""^(2n+1)P_(n-1)=((2n+1)!)/((n+2)!) and ""^(2n-1)P_n=((2n-1)!)/((n-1)!)

If S_(n) , denotes the sum of first n terms of a A.P. then (S_(3n)-S_(n-1))/(S_(2n)-S_(2n-1)) is always equal to

The value of lim _( n to oo) [ (1)/( n +1) + (1)/(n +2) + ...+ (1)/(6n) ] is

sum_(r=1)^(n) tan^(-1)(2^(r-1)/(1+2^(2r-1))) is equal to a) tan^(-1)(2^n) b) tan^(-1)(2)^n-pi/4 c) tan^(-1)(2^(n+1)) d) tan^(-1)(2^(n+1))-pi/4