# Thread: General Term of the Series problem.

1. ## General Term of the Series problem.

Find an expression for the general term of the series below. Assume the starting value of the index, k, is 0. Denote terms such as k! or (2k)! as fact_k or fact_2k. Here is the series...

$\displaystyle (x-8)^4 - \frac{(x-8)^6}{2!} + \frac{(x-8)^8}{4!} - \frac{(x-8)^10}{6!} + ...$

What I get for an answer is ((-1)^(k+2)(x-a)^(2k+4))/(fact_(k+1)).

What I am wondering is why is this wrong? Any help appreciated.

2. Originally Posted by Latszer
Find an expression for the general term of the series below. Assume the starting value of the index, k, is 0. Denote terms such as k! or (2k)! as fact_k or fact_2k. Here is the series...

$\displaystyle (x-8)^4 - \frac{(x-8)^6}{2!} + \frac{(x-8)^8}{4!} - \frac{(x-8)^10}{6!} + ...$

What I get for an answer is ((-1)^(k+2)(x-a)^(2k+4))/(fact_(k+1)).

What I am wondering is why is this wrong? Any help appreciated.
Does it give the correct term corresponding to k = 2 ....?

You might find it easier to get the general term if you first take out a common factor of (x - 8)^4 from the series.

3. The only thing I see is that k+1 factorial should be 2k+1 factorial

4. Originally Posted by Latszer
The only thing I see is that k+1 factorial should be 2k+1 factorial
*Sigh* Does that give you the correct term corresponding to k = 1? Why don't you just follow the advice I gave in my first post.