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# Don't understand

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

Oct 2, 2017

#1
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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 !!.

Oct 2, 2017
#2
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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 ]

Oct 2, 2017
#3
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Don't wait up for me!! I never really learned how to do these "sum" things!!

Oct 2, 2017
#4
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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

Oct 2, 2017
edited by Guest  Oct 2, 2017