A) 21
B) 20
C) 19
D) None
Correct Answer: A
Solution :
[a] \[S=\frac{1}{1-\frac{1}{2}}=2\] \[{{S}_{n}}=\frac{1\left( 1-\frac{1}{{{2}^{n}}} \right)}{1-\frac{1}{2}}=2-\frac{1}{{{2}^{n-1}}}\] Given \[S-{{S}_{n}}<{{10}^{-6}}\] \[\therefore \,\,\,\frac{1}{{{2}^{n-1}}}<{{10}^{-6}}\Rightarrow {{2}^{n-1}}>{{10}^{6}}\] \[\therefore \,\,\,n-1>6{{\log }_{2}}10=\frac{6}{0.3010}n>20\] \[\left[ \because \,\,\,\frac{6}{.3018}<20 \right]\] \[\therefore \,\,\,n=21\]You need to login to perform this action.
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