`1/(1.2)+1/(2.3)+1/(3.4)+...` to `n` terms

the sum of series 1+(1+2)/(2)+(1+2+3)/(3)+...... to n terms

If 1+(1+2)/(2)+(1+2+3)/(3)+.... to n terms is S.Then,s is equal to

lim_ (n rarr oo) [(1) / (1.2) + (1) / (2.3) + (1) / (3.4) + ... + (1) / (n (n + 1))] =

If S_(n)=(1.2)/(3!)+(2.2^(2))/(4!)+(3.2^(3))/(5!)+... upto n terms then the sum infinite terms is

For all quad prove that (1)/(1.2)+(1)/(2.3)+(1)/(3.4)+...+(1)/(n(n+1))=(n)/(n+1)

Find the sum to n terms of the series S_(n)=cot^(-1)(2^(2)+(1)/(2))+cot^(-1)(2^(3)+(1)/(2^(2)))+cot^(-1)(2^(4)+(1)/(2^(3)))+..... upto n terms ?

Find the sum of the following. (1-(1)/(n))+(1-(2)/(n))+(1-(3)/(n))+... up to n terms.

1+(1+2)+(1+2+3)+(1+2+3+4)+ to n terms.