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

Sum of the series 1+(1+2)+(1+2+3)+(1+2+3+4)+... to n terms be 1/m n(n+1)[(2n+1)/k+1] then find the value of k+m

Prove by the method of induction (1)/(1*2)+(1)/(2*3)+(1)/(3*4)+………… upto n terms =(n)/(n+1) where n in N

Sum of n terms of the series 1/(1.2.3.4.)+1/(2.3.4.5) +1/(3.4.5.6)+....

Sum of n terms of the series 1/(1.2.3.4.)+1/(2.3.4.5) +1/(3.4.5.6)+....

FInd the sum of infinite terms of the series 1/(1.2.3)+1/(2.3.4)+1/(3.4.5).....

Find the sum of G.P. : 1-(1)/(3)+(1)/(3^(2))-(1)/(3^(3))+ . . . .. . . . . to n terms.

Find the sum of n terms \ of the series: 1/(1. 2)+1/(2. 3)+1/(3. 4)+...............+1/(n.(n+1))

Find the sum of n terms \ of the series: 1/(1. 2)+1/(2. 3)+1/(3. 4)+dot+1/(ndot(n+1))

If S_(n)=(1.2)/(3!)+(2.2^(2))/(4!)+(3.2^(2))/(5!)+...+ up to n terms, then sum of infinite terms is

Prove the following by using the principle of mathematical induction for all n in N : 1/(1. 2. 3)+1/(2. 3. 4)+1/(3. 4. 5)+...+1/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2))