binomial expansion

**wahhdoe** · February 2nd 2010, 08:06 AM

Hi could somebody please help me.
I really dont understand how to approach this question.

the coefficient of x^2 is 3/8 in the expansion of (1+x/n)^n. find n.

any sort of help would be much appreciated.
thanks.

**Opalg** · February 2nd 2010, 08:34 AM

Originally Posted by wahhdoe

Hi could somebody please help me.
I really dont understand how to approach this question.

the coefficient of x^2 is 3/8 in the expansion of (1+x/n)^n. find n.

The binomial expansion of $\bigl(1+\tfrac xn\bigr)^n$ is

$\Bigl(1+\frac xn\Bigr)^n = 1 + {n\choose1}\Bigl(\frac xn\Bigr) + {n\choose2}\Bigl(\frac xn\Bigr)^2 + \ldots + \Bigl(\frac xn\Bigr)^n.$

You can see from that what the coefficient of $x^2$ is (in terms of n). Put it equal to 3/8 and solve for n.

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