Does it exist?

Calculus Level 2

( ∑ n = 1 ∞ 2 5 n − 1 ) 2 = ? \large \left( \sum_{n=1}^\infty \dfrac2{5^{n-1}} \right)^2 = \, ?

Submit your answer as 0.1 if you think the sum diverges.


The answer is 6.25.

Russel Ryan Floresca by Russel Ryan Floresca , 20, Philippines

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

Mateus Gomes
Feb 13, 2016

∑ n = 1 ∞ 2 5 n − 1 = 10 ∑ n = 1 ∞ 1 5 n ( G P ) = 10 × 1 5 1 − 1 5 = 10 4 \sum_{n=1}^{\infty}\frac{2}{5^{n-1}}=10\sum_{n=1}^{\infty}\frac{1}{5^n}~~(\color{#D61F06}{GP})=10\times\frac{\frac{1}{5}}{1-\frac{1}{5}}=\color{#20A900}{\frac{10}{4}} ( 10 4 ) 2 = 6.25 \Large\color{#3D99F6}{\boxed{\left(\frac{10}{4}\right)^2=6.25}}

4 Helpful 1 Interesting 1 Brilliant 0 Confused
Deepak Kumar
Feb 13, 2016

Should be in Level 1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Please post this as a comment rather than an answer.

Arulx Z - 5 years, 4 months ago

Sorry for that.

Russel Ryan Floresca - 5 years, 4 months ago

But sir, this is kinda rude to say.

Russel Ryan Floresca - 5 years, 4 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...