Difference between revisions of "2008 Mock ARML 2 Problems/Problem 8"
(New page: ==Problem== Given that <math>\sum_{i = 0}^{n}a_ia_{n - i} = 1</math> and <math>a_n > 0</math> for all non-negative integers <math>n</math>, evaluate <math>\sum_{j = 0}^{\infty}\frac {a_j}{...) |
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+ | {{Mock ARML box|year = 2008|n = 2|num-b=7|after=Final Question|source = 206880}} |
Revision as of 08:54, 30 May 2008
Problem
Given that and for all non-negative integers , evaluate .
Solution
We make a conjecture that , where is the th Fibonacci number and we prove that it is so:
We must prove that .
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
2008 Mock ARML 2 (Problems, Source) | ||
Preceded by Problem 7 |
Followed by Final Question | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 |