A) 1
B) 2
C) 3/2
D) 4
Correct Answer: B
Solution :
The sum of infinite arithmetico geometric sequence is \[{{S}_{n}}=\frac{\alpha }{1-r}+\frac{dr}{{{(1-r)}^{2}}}\]. We have. \[{{2}^{1/4}}.\,{{4}^{1/8}}{{.8}^{1/16}}...\] \[={{2}^{1/4}}{{.2}^{2/8}}{{.2}^{3/16}}....\] \[={{2}^{\frac{1}{4}\left[ 1+\frac{2}{3}+\frac{3}{{{2}^{2}}}+.... \right]}}\] \[={{2}^{\frac{1}{4}\left[ \frac{1}{1-\frac{1}{2}}+\frac{1\times \frac{1}{2}}{{{\left( 1-\frac{1}{2} \right)}^{2}}} \right]}}\] \[={{2}^{\frac{1}{4}[2+2]}}=2\]
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