Difference between revisions of "2007 UNCO Math Contest II Problems/Problem 7"

(Created page with "== Problem == (a) Express the infinite sum <math>S= 1+ \frac{1}{3}+\frac{1}{3^2}+ \frac{1}{3^3}+ \cdots</math> as a reduced fraction. (b) Express the infinite sum <math>T=\frac...")
 
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<math>F_n</math> where <math>F_n=F_{n-1}+F_{n-2}</math>.
 
<math>F_n</math> where <math>F_n=F_{n-1}+F_{n-2}</math>.
  
== Solution ==
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== Solution ==  
 
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{{solution}}
  
 
== See Also ==
 
== See Also ==

Revision as of 20:54, 5 December 2016

Problem

(a) Express the infinite sum $S= 1+ \frac{1}{3}+\frac{1}{3^2}+ \frac{1}{3^3}+ \cdots$ as a reduced fraction.

(b) Express the infinite sum $T=\frac{1}{5}+ \frac{1}{25}+ \frac{2}{125}+ \frac{3}{625}+ \frac{5}{3125}+ \cdots$ as a reduced fraction. Here the denominators are powers of $5$ and the numerators $1, 1, 2, 3, 5, \ldots$ are the Fibonacci numbers $F_n$ where $F_n=F_{n-1}+F_{n-2}$.

Solution

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See Also

2007 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions
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