Determine the value of the infinite product
\((2^{1/3})(2^{1/9})(2^{1/27}) \dotsm\)
Enter your answer in the form "\sqrt[a]{b}"
+9519 Suppose you mean the exponents form a geometric sequence.
Just combine the exponents using the formula \(a^m a^n = a^{m+n}\).
\(2^{1/3} \cdot 2^{1/9} \cdot 2^{1/27} \cdots = 2^{1/3 + 1/9 + 1/27 + \cdots}\)
Note that the exponent is now the sum of a geometric sequence. Can you complete it now?
