# Thread: Binomial Theorem Question

1. ## Binomial Theorem Question

Use a binomial expansion to simplify:

a) (10c0)+(10c1)3+(10c2)3^2+...+(10c10)3^10
b) (nc0)-(nc1)+(nc2)-(nc3)+...+(-1)^n (ncn)

c meaning chose

Any help would be greatly appreciated, I seem to be struggling quite alot with this topic but hopefully after this question I will be professional.

2. Originally Posted by Solid8Snake
Use a binomial expansion to simplify:
a) (10c0)+(10c1)3+(10c2)3^2+...+(10c10)3^10
b) (nc0)-(nc1)+(nc2)-(nc3)+...+(-1)^n (ncn)
You know $\displaystyle \left( {1 + x} \right)^{10} = \sum\limits_{k = 0}^{10} {\binom{10}{k}x^k }$. Let $\displaystyle x=3$

3. im not quite sure what you mean. Could you demonstrate with question a so that i get an idea how to apply to b.

thx

4. Do you understand this: $\displaystyle \left( {y + x} \right)^{10} = \sum\limits_{k = 0}^{10} {\binom{10}{k} y^{10-k}x^k } ?$

If you do understand that, then let $\displaystyle y=1~\&~x=3$.
See if the right-hand side is exactly part a.

5. Just in case you're confused with the notation, $\displaystyle {n\choose k}=^nC_k$

6. i understand most of what you posted Plato, however the only part i dont understand is the sigma sign (what does that represent because in school we never learnt that.)

Thx again