Question

1/(5×7) + 1/(7×9) + 1/(9×11) + .........till infinity? ​

Answer 1

Answer:

1/(11×13)

hope it will help you

Answer 2

Answer:

Step-by-step explanation:

The generalized form for n th term of this sequence= $1/(2n-1)(2n+1)(2n+3)$

We can arrange them is such an order,

Let term $n= 1/(2n+1)(2n+3) - 1/(2n+1)(2n-1)$

=$-4/(2n+1)(2n-1)(2n+3)$

Therefore, term $n= 1/-4 [ 1/(2n+1)(2n+3) - 1/(2n+1)(2n-1) ]$

We find this to be a telescopic sum.

Therefore answer is,

$n(n+2)/3(2n+1)(2n+3).$

hope it helps

:)