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2014 CHMMC (Fall)
5
2014 CHMMC Tiebreaker 5 \prod^{\infty}_{n=1} 3^{n/3^n}
2014 CHMMC Tiebreaker 5 \prod^{\infty}_{n=1} 3^{n/3^n}
Source:
March 1, 2024
Radicals
algebra
CHMMC
Problem Statement
Determine the value of
∏
n
=
1
∞
3
n
/
3
n
=
3
3
3
2
3
2
3
3
3
3
.
.
.
\prod^{\infty}_{n=1} 3^{n/3^n}= \sqrt[3]{3} \sqrt[3^2]{3^2} \sqrt[3^3]{3^3} ...
n
=
1
∏
∞
3
n
/
3
n
=
3
3
3
2
3
2
3
3
3
3
...
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