Difference between revisions of "AoPS Wiki:Problem of the Day/September 10, 2011"
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| + | ==Problem== | ||
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> | ||
| + | ==Solution== | ||
| + | The solution to this problem can be found [[AoPSWiki talk:Problem of the Day/September 10, 2011|here]] or by clicking [[AoPSWiki talk:Problem of the Day/September 10, 2011|Discussion]] under "Page Tools" at left. | ||
<noinclude>[[category:Problem of the Day]]</noinclude> | <noinclude>[[category:Problem of the Day]]</noinclude> | ||
Revision as of 08:28, 10 September 2011
Problem
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)
Solution
The solution to this problem can be found here or by clicking Discussion under "Page Tools" at left.
