Difference between revisions of "AoPS Wiki talk:Problem of the Day/September 10, 2011"
(Created page with "Let <cmath>S=\frac{F_1}{3}+\frac{F_2}{9}+\frac{F_3}{27}+\frac{F_4}{81}+\frac{F_5}{243}+\cdots</cmath> Multiplying through by 1/3, we see <cmath>\frac{1}{3}S=\frac{F_1}{9}+\frac{F...") |
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<cmath>S=\frac{F_1}{3}+\frac{F_2}{9}+\frac{F_3}{27}+\frac{F_4}{81}+\frac{F_5}{243}+\cdots</cmath> | <cmath>S=\frac{F_1}{3}+\frac{F_2}{9}+\frac{F_3}{27}+\frac{F_4}{81}+\frac{F_5}{243}+\cdots</cmath> |
Latest revision as of 08:24, 10 September 2011
Solution
Let Multiplying through by 1/3, we see and, noting that , we subtract: and, multiplying through by 9, we see S in the right side: and thus and .