Question

2^1/4 . 4^1/8 . 8^1/16 ….. is equal to –

• A. 1
• B. 2
• C. 3/2
• D. None of these

Answer 1

Answer: (B)

2

Answer 2

Value = 2^{1/4 + 2/8 + 3/8+…..+} = 2^s

Where S = $\frac{1}{4}$+$\frac{2}{8}$+$\frac{3}{16}$+ …..

$\frac{1}{2}$s = $\frac{1}{8}$+$\frac{2}{16}$+$\frac{3}{32}$+…..

\ s – $\frac{1}{2}$s = $\frac{1}{4}$+$\frac{1}{8}$+$\frac{1}{16}$+……=$\frac{1/4}{1 - 1/2}$= $\frac{1}{2}$

Ž s = 1

Ž 2^s = 2.