Partial Sums for Series: Solving Using Partial Fractions

[gkamal]

Homework Statement

[/B]

Homework Equations

an= bn - bn+1 which is already in the problem

The Attempt at a Solution

[/B]
i did partial fractions but then i got stuck at

16/12 [4n-5] - 16/12 [4n+7] that part about bn confuses me please someone explain in detail

 

[Mark44]

Homework Statement

[/B]

Homework Equations

an= bn - bn+1 which is already in the problem

The Attempt at a Solution

[/B]
i did partial fractions but then i got stuck at

16/12 [4n-5] - 16/12 [4n+7] that part about bn confuses me please someone explain in detail

Where's the equation you're working with?
Starting from $\frac{16}{16n^2 + 8n - 35} = \frac{A}{4n - 5} + \frac{B}{4n + 7}$, multiply both sides by $16n^2 + 8n - 35$ to clear out all of the denominators. Then solve for the constants A and B.

 

[gkamal]

i did and i get 16/12 for A and - 16/12 for B as i indicated above the problem is what is the next step

 

[vela]

I think there's a typo in the problem. It should say $a_n = b_n - b_{n+3}$.