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**Sum of convergent series HELP!!**

## Homework Statement

Find the sum of the convergent series -

the sum of 6 / (n+7)(n+9) from n=1 to infinity (∞)

A) 31/24

B) 45/56

C) 8/11

D) 17/24

E) 23/24

**2. The attempt at a solution**

I was looking in the book and they had one example that was kinda close so i tried to follow it and i did this....

= 6 times the sum of (1/(n+7))-(1/n+9))

= 6 times (1/8-1/10)+(1/9-1/11)... and so on

but that got me nowhere.

I tried plugging this into my calculator sum(seq(6/(x+7)(x+9),x,1,999,1)

and i got .7023779 which is the closest to answer D --> .70833333

but that's only up to term 999 and how do i know that the series won't get bigger than 17/24?

i found that up to the 7,490th term the sum is .7075417. which is closer so i'm going to go with answer D. :)

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