Question

\(\frac{2^1}{4} \cdot \frac{2^2}{8} \cdot \frac{2^3}{16} \cdot \frac{2^4}{32} \cdots\) is equal to

• A. 1
• B. 2
• C. \(3/2\)
• D. 5/2

Hint:

Convert products to sums of exponents.

Answer 1

The Correct Option is B

Exponents form \(\sum_{k \ge 1} \frac{k}{2^{k+1}} = 1\).

Hence product = \(2^1 = 2\).