Find the sum `1+1/(1+2)+1/(1+2+3)+..........+1/(1+2+3+.........+n)dot`

Find the sum : (a) 1 1/4+1 1/2 (b) 1 1/4+2 1/3

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 1+2.2+3.2^(2)+4.2^(3)+....+n.2^(n-1)

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

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

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

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