A) \[3\]
B) \[4\]
C) \[\frac{7}{2}\]
D) \[\frac{9}{2}\]
Correct Answer: C
Solution :
Let\[S=2+\frac{1}{2}+\frac{1}{3}+\frac{1}{{{2}^{2}}}+\frac{1}{{{3}^{2}}}+\frac{1}{{{2}^{3}}}+\frac{1}{{{3}^{3}}}+...\] \[=\left( 1+\frac{1}{2}+\frac{1}{{{2}^{2}}}+\frac{1}{{{3}^{2}}}+... \right)\] \[=\frac{1}{1-\frac{1}{2}}+\frac{1}{1-\frac{1}{3}}\] \[(\because \]\[GP\]series) \[=\frac{2}{1}+\frac{3}{2}\] \[=\frac{7}{2}\]You need to login to perform this action.
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