2017 AMC 10A Problems/Problem 1
Contents
Problem
What is the value of ?
Solution 1
Notice this is the term in a recursive sequence, defined recursively as Thus:
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Solution 2
Starting to compute the inner expressions, we see the results are . This is always less than a power of . The only admissible answer choice by this rule is thus .
Solution 3
Working our way from the innermost parenthesis outwards and directly computing, we have .
Solution 4
If you distribute this you get a sum of the powers of . The largest power of in the series is , so the sum is .
Solution 5
.
Solution 6 (quickest)
Notice that . Substituting for , we get
Video Solution
~savannahsolver
See Also
2017 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
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All AMC 10 Problems and Solutions |
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