# Thread: Finding terms with given binomial?? Binomial Theorem?

1. ## Finding terms with given binomial?? Binomial Theorem?

Hi, I forgot how to plug in the binomial Theorem.

My two problems:

1) Find the 5th term of the given binomial. (a+ square root of (b))^9

2) Find the 6th term of the given binomial (p/2-q/2)^9

2. ## Re: Finding terms with given binomial?? Binomial Theorem?

$(a+b)^n = \displaystyle{\sum_{k=0}^n}\begin{pmatrix}n \\ k\end{pmatrix}a^k b^{n-k}$

3. ## Re: Finding terms with given binomial?? Binomial Theorem?

Originally Posted by math951
My two problems:
1) Find the 5th term of the given binomial. (a+ square root of (b))^9
2) Find the 6th term of the given binomial (p/2-q/2)^9
I and most who have done work for the testing community will not answer these.
The fact is there is no one correct answer.

In the expansion ${(a + b)^9} =\displaystyle \sum\limits_{k = 0}^9 {\dbinom{9}{k}{a^k}{b^{9 - k}}}$ has ten terms.
BUT the expansion ${(a + b)^9} =\displaystyle \sum\limits_{k = 0}^9 {\dbinom{9}{k}{a^{9-k}}{b^{k}}}$ is the equivlant expansion, just in a different order.
The sixth term in the first first expansion which is not the sixth term in the second expansion.
So which is the sixth term in $(a+b)^9~?$

You may show your teacher this if you like.