Series expansion/algebra problem

  • Thread starter BOAS
  • Start date
  • #1
555
19
Hi,

i'm revising series expansions and my problem has arisen from an example in my text book, but it's not directly related to the series expansion itself. It's more of an algebra question, where they've made a rearrangement I can't follow...

Homework Statement



If [itex]n[/itex] is a positive integer find the coefficient of [itex]x^{r}[/itex] in the expansion of [itex](1 + x)(1 - x)^{n}[/itex] as a series of ascending powers of x.

Homework Equations





The Attempt at a Solution



The solution starts by stating the following expressions are equivalent.

[itex](1 + x)(1 - x)^{n} \equiv (1 - x)^{n} + x(1 - x)^{n}[/itex]

If I take this statement to be true, I can follow through the rest of the example without a hitch, but I just can't see what they've done here.

Thanks for any help you can give,

BOAS.
 

Answers and Replies

  • #2
3,816
92
Hi,

i'm revising series expansions and my problem has arisen from an example in my text book, but it's not directly related to the series expansion itself. It's more of an algebra question, where they've made a rearrangement I can't follow...

Homework Statement



If [itex]n[/itex] is a positive integer find the coefficient of [itex]x^{r}[/itex] in the expansion of [itex](1 + x)(1 - x)^{n}[/itex] as a series of ascending powers of x.

Homework Equations





The Attempt at a Solution



The solution starts by stating the following expressions are equivalent.

[itex](1 + x)(1 - x)^{n} \equiv (1 - x)^{n} + x(1 - x)^{n}[/itex]

If I take this statement to be true, I can follow through the rest of the example without a hitch, but I just can't see what they've done here.

Thanks for any help you can give,

BOAS.

Let ##(1-x)^n=a##, then ##a(1+x)=a+ax##. Do you see now? :)
 
  • #3
555
19
Let ##(1-x)^n=a##, then ##a(1+x)=a+ax##. Do you see now? :)

Perfectly.

Thank you!
 

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