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OpenStudy (anonymous):

find the first four terms of the binomial expansion of (1-x)^-5

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OpenStudy (anonymous):

as in power series expansion?

OpenStudy (anonymous):

yes please

OpenStudy (anonymous):

\[f(x)=\frac{1}{(1-x)^5}\]we need \[f(0), f'(0), f''(0), f^{(3)}(0),f^{(4)}(0)\] \

OpenStudy (anonymous):

i don't think there is a snap way to do it.

OpenStudy (anonymous):

\[f(0)=1\] \[f'(x)=5(1-x)^{-6}\] so \[f'(0)=5\] \[f''(x)=30(1-x)^{-7}\] so \[f''(0)=30\] \[f^{(3)}(x)=210(1-x)^{-8}\] and \[f^{(3)}(0)=210\]

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OpenStudy (anonymous):

expansion coefficients are \[\frac{f^{(n)}(0)}{n!}\] so we get \[1+5x+15x^2+35x^4+\]

OpenStudy (anonymous):

oh you have one more but it is clear right? next one will be \[\frac{8\times 210}{4!}\]

OpenStudy (anonymous):

i get 70

OpenStudy (anonymous):

Been struggling with this for awhile now , thanks alot, appreciate it :)

OpenStudy (anonymous):

yw hope steps are clear

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OpenStudy (anonymous):

yes, thanks, it makes more sense to me now.

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