`S_n=(1. 2)/3+(2. 3)/(3^2)+(3. 4)/(3^3)......oo,` then `4S` is

If S=(1)/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+...."to "oo , then S =

If S=(1)/(1+1^(2)+1^(4))+(2)/(1+2^(2)+2^(4))+(3)/(1+3^(2)+3^(4))+......oo then find the value of 14S.

Let S denote sum of the series 3/(2^3)+4/(2^4 .3)+5/(2^6 .3)+6/(2^7 .5)+ ...... oo Then the value of S^(-1) is __________.

If 1/1^3 + (1+2)/(1^3+2^3)+(1+2+3)/(1^3+2^3+3^3) +.......n terms then lim_(n->oo) [S_n]

Which of the following statement(s) is/are correct? 1+(2)/(2)+(3)/(2^(2))+(4)/(2^(3))+.........+oo=4

If (1)/(1^(3))+(1+2)/(1^(3)+2^(3))+(1+2+3)/(1^(3)+2^(3)+3^(3))+......n terms then lim_(n rarr oo)[S_(n)]