2020 AMC 10A Problems/Problem 21
There exists a unique strictly increasing sequence of nonnegative integers such that
What 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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