Calculate

May 2009
596
31
ALGERIA
Calculate
\(\displaystyle
2^{\frac{1}{4}}\times 2^{\frac{1}{8}}\times 2^{\frac{1}{16}}\times.... \times .....
\)
 
Last edited:

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
Calculate
\(\displaystyle
2^{\frac{1}{4}}\times 2^{\frac{1}{8}}\times 2^{\frac{1}{16}}\times \times .....
\)
\(\displaystyle 2^2\times 2^2=2^{2+2}\)

\(\displaystyle \sum_{n=2}^{\infty}2^{x}\) where \(\displaystyle x=\frac{1}{2^n}\)
 

Soroban

MHF Hall of Honor
May 2006
12,028
6,341
Lexington, MA (USA)
Hello, dhiab!

Calculate : .\(\displaystyle 2^{\frac{1}{4}}\times 2^{\frac{1}{8}}\times 2^{\frac{1}{16}}\times \hdots\)

\(\displaystyle \text{We have: }\;2^{\overbrace{(\tfrac{1}{4}+\tfrac{1}{8}+ \tfrac{1}{16}+ \hdots)}^{\text{geometric series}}} \;=\;2^{\frac{1}{2}} \;=\;\sqrt{2}\)