- #1

- 173

- 2

## Homework Statement

For ##n>0##, the expansion of ##(1+mx)^{-n}## in ascending powers of ##x## is ##1+8x+48x^{2}+...##

(a) Find the constants ##m## and ##n##

(b) Show that the coefficient of ##x^{400}## is in the form of ##a(4)^{k}##, where ##a## and ##k## are real constants.

## Homework Equations

Binomial expansion

## The Attempt at a Solution

I have expanded the series using binomial theorem, and compared each coefficient. Then I solved them using simultaneous equation. That works out to be ##m=-4, n=2##.

(b) I know the binomial coefficient is ##\frac{n(n-1)(n-2)...(n-r+1)}{r!}##, though I'm stuck on that... :(

Last edited: