1. Find term

nb

2. I'm troubled by this.

2) You have the right index for a moment, but then lose it.
3) Did you separate a and b just to confuse yourself?
4) You are asked for the coefficient. Why give the entire term?

The first term has C(10,0). The second C(10,1)...The sixth has C(10,5).
The first term has (ab)^10. The second (ab)^9...The sixth has (ab)^5.

It wouldn't hurt to write out the entire expansion, at least once, just so you can see it all.

3. I really dislike this question. I was able to have the sort of question excluded from a major contest paper.

Who is to say what the fifth term is?

$\sum\limits_{k = 0}^N { {{N} \choose {k}} x^k y^{N - k} } = \sum\limits_{k = 0}^N { {{N} \choose {k}} x^{N - k} y^k }$.

We might be able to ask for the middle term if N is even.

4. You are treating ab as if they were TWO different integers rather then one.

5. You seem to be asking the same question just different coefficients in different threads so i'll do all the 10

ab^10-30ab^9+405ab^8-3240ab^7+17010ab^6-61236ab^5+153090ab^4-262440ab^3+295245ab^2-196830ab+59049

6. Originally Posted by Plato
Who is to say what the fifth term is?
Right. I'm usually backwards from the way it appears in most textbooks.