2020 AMC 10A Problems/Problem 21
There exists a unique strictly increasing sequence of nonnegative integers such thatWhat is
Solution
First, replace as . Then, the given equation becomes . Now consider only . This equals . Note that equals , since the sum of a geometric sequence is . Thus, we can see that forms the sum of 17 different powers of 2. Applying the same thing to each of , , and so on. This gives us . Our answer is .
~seanyoon777
See Also
2020 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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