Question

Find the sum of 1+1/(1+2)+1/(1+2+3)....uto n terms

Answer 1

Last term = 1/(1+2+3+4+.......+n)=2/n(n+1)

Summession of tn term = 2× sum of 1/n(n+1) = 2×sum of (1/n -1/(n+1))
= 2× (1+1/2+1/3+.....+1/n -1/2-1/3-1/4-...-1/n -1/n+1)
All the terms cancel except 1 and 1/n+1
Sum = 2×(1-1/n+1) = 2n/ n+1