Question

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

Answer 1

as in power series expansion?

Answer 2

yes please

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

i get 70

Answer 9

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

Answer 10

yw hope steps are clear

Answer 11

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