(x+1/x)power N

Question

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$${\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{x}}}}\right)}^{{\mathtt{N}}}$$

If the fifth term in this expansion is independant of X, find the value of N

Guest Jun 28, 2015

+33615

+10

Best Answer

$$(x+\frac{1}{x})^N=x^N+Nx^{N-1}x^{-1}+\frac{N(N-1)}{2!}x^{N-2}x^{-2}+...$$

The fifth term will therefore contain x^N-4x^-4 or x^N-8. For this to be independent of x we must have N - 8 = 0 or N = 8

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Alan Jun 29, 2015

Alan · Answer 1 · 2015-06-29T07:24:25

$$(x+\frac{1}{x})^N=x^N+Nx^{N-1}x^{-1}+\frac{N(N-1)}{2!}x^{N-2}x^{-2}+...$$

The fifth term will therefore contain x^N-4x^-4 or x^N-8. For this to be independent of x we must have N - 8 = 0 or N = 8

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