Real doubt!

Level pending

∑ n = 0 ∞ 1 ( 2 − 1 ) 2 n = 2 1 − 2 2 \sum_{n=0}^\infty \frac {1}{(\sqrt{2}-1)\sqrt {2^n}}= \frac {\sqrt {2}}{1-2\sqrt{2}}

false true

Giancarlo Miragliotta by Giancarlo Miragliotta , 56, Brazil

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.

1 solution

Eli Ross Staff
Dec 16, 2015

While you could use a Geometric Progression Sum to compute the sum on the left-hand-side, I prefer this quicker argument:

All of the terms in the sum are positive, but the right-hand-side is negative. This is impossible.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...