A) 1
B) 0
C) Non-existent
D) None of these
Correct Answer: B
Solution :
| \[\underset{n\to \infty }{\mathop{\lim }}\,\left[ \frac{1}{2}+\frac{1}{{{2}^{2}}}+.....+\frac{1}{{{2}^{n}}} \right]\] |
| \[\underset{n\to \infty }{\mathop{\lim }}\,\,\,\,\left[ \frac{1/2(1-1/{{2}^{n}})}{1-\frac{1}{2}} \right]\] |
| \[\because \,\,\,\,n\to \infty \,\,1-1/{{2}^{n}}<1\] |
| \[\therefore \,\,\,\,\underset{n\to \infty }{\mathop{\lim }}\,\left[ 1-\frac{1}{{{2}^{n}}} \right]=0\] |
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