+0  
 
0
88
4
avatar

Evaluate the sum \[\frac{1}{3^1} + \frac{2}{3^2} + \frac{3}{3^3} + \cdots + \frac{k}{3^k} + \cdots \]

Guest Oct 2, 2017
Sort: 

4+0 Answers

 #1
avatar
0

1/3 + 2/3^2 + 3/3^3 + 4/3^4 + 5/3^5 +............+ k/3^k =3/4

OK, CPhill or hectictar: use your brilliant algebraic knowledge to prove this. I can't !!.

Guest Oct 2, 2017
 #2
avatar+79843 
0

I don't know how to prove this.....but maybe hectictar does......if not.....hang on for heureka........he's usually pretty good at these kind of things  !!!!

 

[ I always learn something from his answers ]

 

 

cool cool cool

CPhill  Oct 2, 2017
 #3
avatar+5555 
0

Don't wait up for me!! I never really learned how to do these "sum" things!!

hectictar  Oct 2, 2017
 #4
avatar+889 
0

Consider the infinite Geometric series \(\displaystyle \frac{1}{x}+\frac{1}{x^{2}}+\frac{1}{x^{3}}+\dots\)  .

Its sum to infinity (I think that there is a mistake in the question, there should be a plus sign and a series of dots after that last term), is \(\displaystyle \frac{1}{x-1}\).

Equate the two, differentiate both sides, and then substitute x = 3.

 

Tiggsy

Bertie  Oct 2, 2017
edited by Guest  Oct 2, 2017

4 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details