Difference between revisions of "2007 UNCO Math Contest II Problems/Problem 7"
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| − | Part A: Knowing that the formula for an infinite geometric series is <math>A/(1 - r)</math>, where <math>A</math> and <math>r</math> are the first term and common ratio respectively, we compute <math>1/(1 - 1/3) = 3/2</math>, and | + | Part A: Knowing that the formula for an infinite geometric series is <math>A/(1 - r)</math>, where <math>A</math> and <math>r</math> are the first term and common ratio respectively, we compute <math>1/(1 - 1/3) = 3/2</math>, and we have our answer of <math>2/3</math>. |
Revision as of 20:05, 5 December 2016
Problem
(a) Express the infinite sum 
as a reduced fraction.
(b) Express the infinite sum 
as a reduced fraction. Here the denominators are powers of 
and the numerators 
are the Fibonacci numbers
where 
.
Solution
Part A: Knowing that the formula for an infinite geometric series is 
, where 
and 
are the first term and common ratio respectively, we compute 
, and we have our answer of 
.
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See Also
| 2007 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| 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 | ||
