" 3."1+(1)/((1+2))+(1)/((1+2+3))+...+(1)/((1+2+3+...n))=(2n)/((n+1))

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

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

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

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

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)))

For all ngt=1 , prove that , (1)/(1.2) + (1)/(2.3) + (1)/(3.4) + ……+ (1)/(n(n+1)) = (n)/(n+1)

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

Statement -1: (1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+ . . . .+(n^(2))/((2n-1)(2n+1))=(n(n+1))/(2(2n+1)) Statement -2: (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+ . . . .+(1)/((2n-1)(2n+1))=(1)/(2n+1)

Statement -1: (1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+ . . . .+(n^(2))/((2n-1)(2n+1))=(n(n+1))/(2(2n+1)) Statement -2: (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+ . . . .+(1)/((2n-1)(2n+1))=(1)/(2n+1)