# Binomial expression help!

• Jan 30th 2006, 04:25 AM
Confuzzled?
Binomial expression help!
Find the first three terms in these expansions in ascending powers of x
a) (x+1/x)^6

b) In the expansion of (1+x/2)^n in ascending powers of x the coefficent of x^2 is 30. Find n.

Thanks in advance if you can help
• Jan 30th 2006, 05:55 AM
CaptainBlack
Quote:

Originally Posted by Confuzzled?
Find the first three terms in these expansions in ascending powers of x
a) (x+1/x)^6

$\displaystyle (x+1/x)^6=(1/x)^6+6(1/x)^5x+\frac{6\times 5}{2}(1/x)^4 x^2+...$

$\displaystyle (x+1/x)^6=x^{-6}+6x^{-4}+15x^{-2}+...$

RonL
• Jan 30th 2006, 06:08 AM
CaptainBlack
Quote:

Originally Posted by Confuzzled?
b) In the expansion of (1+x/2)^n in ascending powers of x the coefficent of x^2 is 30. Find n.

$\displaystyle (1+x/2)^n =1+n(x/2)+\frac{n(n-1)}{2}(x/2)^2+...$

So the coeff of $\displaystyle x^2$ in the expansion is:

$\displaystyle \frac{n(n-1)}{8}=30$,

which has solutions $\displaystyle n=-15$ or $\displaystyle n=16$.

I presume there is an implicit assumption that $\displaystyle n \ge 1$ so
the answer would be $\displaystyle n=16$.

RonL
• Jan 30th 2006, 07:04 AM
Confuzzled?
Thank you so much!