Difference between revisions of "2022 AMC 12A Problems/Problem 8"
Phuang1024 (talk | contribs) (Created solution.) |
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Thus, our answer is <math>10 ^ \frac{1}{2} = \boxed{(A) \sqrt{10}}</math> | Thus, our answer is <math>10 ^ \frac{1}{2} = \boxed{(A) \sqrt{10}}</math> | ||
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+ | - phuang1024 |
Revision as of 20:51, 11 November 2022
Problem
The infinite product
evaluates to a real number. What is that number?
Solution
We can write as
. Similarly,
.
By continuing this, we get the form
which is
.
Using the formula for an infinite geometric series , we get
Thus, our answer is
- phuang1024