Math Is Fun Forum

scs_t6

Member

Registered: 2016-07-07

Posts: 2

help with understanding an equation

Hi

This is my first post here.

I have a question regarding the equation below. How do I get from line 1 to line 2?  I mean the part (1-e^x)^(-1) = (1+e^x+e^2x+e^3x+...)

Thanks for help.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: help with understanding an equation

hi scs_t6

Welcome to the forum.

This is an application of (Newton's) generalised binomial expansion.  You'll find it here:

https://en.wikipedia.org/wiki/Binomial_ … al_theorem

About half way down the page.

Hope that helps,

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

scs_t6

Member

Registered: 2016-07-07

Posts: 2

Re: help with understanding an equation

Thanks! This helps, I see it now.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: help with understanding an equation

I mean the part (1-e^x)^(-1) = (1+e^x+e^2x+e^3x+...)

How that was done would depend on the fellows age and his background. If he was around say 100 years old he would remember the Abramowitz Stegun book and the formula to invert a power series given in the early chapters. If he is a young fellow he probably would have used Mathematica and just failed to mention that.

But, if he was a generatingfunctionologist or a baby combinatoricist he would do it like this:

Remembering:

so he would substitute y = e^x and say

which when he substituted back

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.