Infinite Product Needs Simplifying.

Calculus Level pending

Simplify the infinite product (1+x)(1+x^2)(1+x^4)(1+x^8)(1+x^16)..., given |x| < 1.

1 1/(1+x) 2 1/(1-x) (1-x)

Emma Ask by Emma Ask , 23, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

You need to clarify the typo

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Oh, sorry.

Emma Ask - 6 years ago
Emma Ask
Jun 7, 2015

Let P = (1+x)(1+x2)(1+x4)(1+x8)(1+x16)...

Then (1-x)P = (1-x)(1+x)(1+x2)(1+x4)(1+x8)(1+x16)... = (1-x2)(1+x2)(1+x4)(1+x8)(1+x16)... = (1-x4)(1+x4)(1+x8)(1+x16)... = (1-x8)(1+x8)(1+x16)... = ... = 1

Since (1-x)P = 1, it follows that P = 1/(1-x)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...