`1/(1. 3.5)+1/(3. 5.7)+...`

Find the sum of the series 1/1.3+2/(1.3.5)+3/(1.3.5.7) ...upto infinity

Prove by the method of induction, (1)/( 1.3) + (1)/( 3.5) + (1)/( 5.7) + . . . + (1)/( (2n - 1)(2n + 1)) = (n)/(2 n +1)

Find the sum to n terms of the series: 1/(1. 3)+1/(3. 5)+1/(5. 7)+

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)

Find the sum to n terms of the series: (1)/(1.3)+(1)/(3.5)+(1)/(5.7)+...

(1)/(1.3) + (1)/(3.5) + (1)/(5.7) + …. (n-3) terms

(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+....(n-1)terms

(1)/(1 . 3)+(1)/(3 . 5)+(1) /(5 . 7)+.. to n terms =

lim_(n rarr oo){(1)/(1.3)+(1)/(3.5)+(1)/(5.7)+....+(1)/((2n+1)(2n+3 ))