A) \[{{2}^{\frac{1}{2}}}\]
B) \[{{2}^{\frac{1}{4}}}\]
C) \[2\]
D) \[1\]
Correct Answer: A
Solution :
[a] \[{{2}^{\frac{1}{4}}}.\,\,{{4}^{\frac{1}{16}}}.\,\,{{8}^{\frac{1}{48}}}......\] \[={{2}^{\frac{1}{4}}}.\,\,{{2}^{\frac{1}{8}}}.\,\,{{2}^{\frac{1}{16}}}........\] \[={{2}^{\left( \frac{1}{4}+\frac{1}{8}+\frac{1}{16}+..... \right)}}\] \[={{2}^{\frac{1/4}{1-1/2}}}\] \[={{2}^{\frac{1}{2}}}=\sqrt{2}\]
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