Difference between revisions of "AoPS Wiki:Problem of the Day/September 10, 2011"
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Let <math>F_0 = 0</math>, <math>F_1 = 1</math>, and <math>F_n = F_{n - 1} + F_{n - 2}</math>. Find the value of the infinite sum <cmath>\sum_{n=1}^{\infty}\frac{F_n}{3^n}=\frac{1}{3} + \frac{1}{9} + \frac{2}{27} + \cdots + \frac{F_n}{3^n} + \cdots.</cmath> | Let <math>F_0 = 0</math>, <math>F_1 = 1</math>, and <math>F_n = F_{n - 1} + F_{n - 2}</math>. Find the value of the infinite sum <cmath>\sum_{n=1}^{\infty}\frac{F_n}{3^n}=\frac{1}{3} + \frac{1}{9} + \frac{2}{27} + \cdots + \frac{F_n}{3^n} + \cdots.</cmath> | ||
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<noinclude>[[category:Problem of the Day]]</noinclude> | <noinclude>[[category:Problem of the Day]]</noinclude> | ||
Revision as of 08:48, 10 September 2011
Let 
, 
, and 
. Find the value of the infinite sum ![\[\sum_{n=1}^{\infty}\frac{F_n}{3^n}=\frac{1}{3} + \frac{1}{9} + \frac{2}{27} + \cdots + \frac{F_n}{3^n} + \cdots.\]](http://latex.artofproblemsolving.com/5/6/4/564dc1e566f0529b48bec637e37a44d9e6b10411.png)
