2011/059) For all n>= 1 , prove that:- (1)+(1/1+2) + (1/1+2+3)+ ....... + (1/1+2+3+......+n)=(2n/n+1)

this type of sum come under telescopic sum

k th term = 1/(1+2 +3 + ... k) = 2/(k(k+i) = 2 * ( 1/k - 1/(k+1))

1st term = 2(1/1 - 1/2)
2nd term = 2(1/2 - 1/3)

nth term = 2( 1/n - 1/(n+1))

sum (all terms except 1st and last cancel) = 2/(1/1- 1/(n+1)) = 2n/(n+1)