1952 AHSME Problems/Problem 50
Problem
A line initially 1 inch long grows according to the following law, where the first term is the initial length.
![\[1+\frac{1}{4}\sqrt{2}+\frac{1}{4}+\frac{1}{16}\sqrt{2}+\frac{1}{16}+\frac{1}{64}\sqrt{2}+\frac{1}{64}+\cdots\]](http://latex-new.aopstest.com/a/2/5/a25241611d30e4eef36fe597a9800f9723ec4a5b.png)
If the growth process continues forever, the limit of the length of the line is:
Solution
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See also
| 1952 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 49 |
Followed by Problem 50 | |
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