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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Latest revision as of 08:50, 10 September 2011
Let , , and . Find the value of the infinite sum