Recursive sequence terms don't cancel

[whompa]

Homework Statement

The following series is a telescopic series. Find the exact sum of the series by performing a partial fraction decomposition and generalizing the formula for the nth partial sum S_n.

Homework Equations

The Attempt at a Solution

3n + 2 = A(n+1)(n+2) + B(n)(n+2) + C(n)(n+1)
n = 0 → 2 = 2A → A = 1
n = -1 → -1 = -B → B = 1
n = -2 → -4 = 2C → C = -2

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

=> S_n = ... = 1 + 1/2 + 1/3 + ... + 1/n + 2/3 + 2/5 + 2/7 + ... + 1/(2n + 1)

I don't see the terms cancel. Did i do something wrong?

Thanks

 

[susskind_leon]

You forgot about the minus, dude! C=-2 :D

 

[whompa]

Ah, sorry about that, i did have a minus in my original work, typo o_o