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

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- Jan 30th 2006, 04:25 AMConfuzzled?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 AMCaptainBlackQuote:

Originally Posted by**Confuzzled?**

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

RonL - Jan 30th 2006, 06:08 AMCaptainBlackQuote:

Originally Posted by**Confuzzled?**

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 AMConfuzzled?
Thank you so much!