please find coefficient

**oceanmd** · December 7th 2007, 12:41 AM

nb

**Jhevon** · December 7th 2007, 12:53 AM

Originally Posted by oceanmd

I do not even know how to touch this problem. Please help.
Find coefficient of x^0 in the expansion of (x^2+1\x)^12

Thank you

we have $\left( x^2 + x^{-1} \right)^{12}$

using $(a + b)^n = \sum_{k = 0}^{n}{n \choose k}a^kb^{n - k}$ we have:

$\left( x^2 + \frac 1x \right)^{12} = \left( x^2 + x^{-1} \right)^{12} = \sum_{k = 0}^{12}{12 \choose k}x^{2k}x^{k - 12} = \sum_{k = 0}^{12}{12 \choose k}x^{3k - 12}$

now continue

**Jhevon** · December 7th 2007, 01:05 AM

Originally Posted by oceanmd

3k-12=0; k=4
coefficient is 495.
Thank you

yes

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