[" दी मह अखला के "n" पदो का योगफत्त झता वमिकर "],[1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2))+]

1*2+2*2^(2)+3*2^(3)+*2^(n)=(n-1)2^(n+1)+2

Let H_(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n) , then the sum to n terms of the series (1^(2))/(1^(3))+(1^(2)+2^(2))/(1^(3)+2^(3))+(1^(2)+2^(2)+3^(2))/(1^(3)+2^(3)+3^(3))+ . . . , is

Prove that 1^(2)+2^(2)+3^(2)+.....+n^(2)=(n(n+1)(2n+1))/6

(i) 1+(1+2)+(1+2+3)+………. to n terms. (ii) 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2))+ ………………to n terms.

a_ (n) = (1+ (1) / (n ^ (2))) (1+ (2 ^ (2)) / (n ^ (2))) ^ (2) (1+ (3 ^ ( 2)) / (n ^ (2))) ^ (3) ......... (1+ (n ^ (2)) / (n ^ (2))) ^ (n) then lim_ (n rarr oo) a_ (n) ^ (- (1) / (n ^ (2))) is equal to

Let H_(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n) , then the sum to n terms of the series (1^(2))/(1^(3))+(1^(2))/(1^(3))+(2^(2))/(2^(3))+(1^(2)+2^(2)+3^(2))/(1^(3)+2^(3)+3^(3))+ . . . , is

Prove that : 1^(2)+2^(2)+3^(2)+...+n^(2)=(n(n+1)(2n+1))/(6)

lim_ (n rarr oo) [(1+ (1) / (n ^ (2)))) (1+ (2 ^ (2)) / (n ^ (2))) (1+ (3 ^ (2) ) / (n ^ (2))) ...... (1+ (n ^ (2)) / (n ^ (2)))] ^ ((1) / (n))

show that (3*2^(n+1)+2^(n))/(2^(n+2)-2^(n-1))=2