Repeating Roots

Algebra Level 3

What is the value of 1 1 1 1 1 1 1 ⋯ \displaystyle \sqrt{1 \sqrt{1 \sqrt{1 \sqrt{1 \sqrt{1 \sqrt{1 \sqrt{1 \cdots}}}}}}} ?


The answer is 1.

. . by . . , 14, South Korea

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1 solution

. .
Feb 10, 2021

1 1 1 1 1 1 1 ⋯ \sqrt{1 \sqrt{1 \sqrt{1 \sqrt{1 \sqrt{1 \sqrt{1 \sqrt{1 \cdots}}}}}}} is equal to 1 \sqrt{1} . So it is ± 1 \pm 1 , but the problem said that the answer is a ≥ 0 a \geq 0 , so the answer is 1 1 . ( a a means the answer.)

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