2024 AMC 10B Problems/Problem 23
Contents
[hide]Problem
Solution 1
Brute forcing gets you B) 319
Solution 2
Plug in a few numbers to see if there is a pattern. List out a few Fibonacci numbers, and then try them on the equation. You'll find that and The pattern is that then ten fractions are in their own Fibonacci sequence with the starting two terms being and , which can be written as for Summing the first ten terms, you arrive at the answer
See also
2024 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 22 |
Followed by Problem 24 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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