A) 2
B) ?1
C) 1
D) 3
Correct Answer: C
Solution :
\[y=\underset{n\to \infty }{\mathop{\lim }}\,\,\frac{1}{2}+\frac{1}{{{2}^{2}}}+\frac{1}{{{2}^{3}}}+.......+\frac{1}{{{2}^{n}}}=\underset{n\to \infty }{\mathop{\lim }}\,\,\,\frac{1}{2}\,\frac{\left[ 1-{{\left( \frac{1}{2} \right)}^{n}} \right]}{\left( 1-\frac{1}{2} \right)}\] \[\underset{n\to \infty }{\mathop{\lim }}\,\,\left[ 1-\frac{1}{{{2}^{n}}} \right]=1-0=1\]
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