A) \[\frac{16}{35}\]
B) \[\frac{11}{8}\]
C) \[\frac{35}{16}\]
D) \[\frac{8}{16}\]
Correct Answer: C
Solution :
Let\[S=1+\frac{4}{5}+\frac{7}{{{5}^{2}}}+\frac{10}{{{5}^{3}}}+....\infty \] \[\frac{1}{5}S=\frac{1}{5}+\frac{4}{{{5}^{2}}}+\frac{7}{{{5}^{3}}}+....\infty \] Subtracting, \[\frac{4}{5}S=1+3\left( \frac{1}{5}+\frac{1}{{{5}^{2}}}+\frac{1}{{{5}^{3}}}+.....\infty \right)\] \[=1+3.\frac{5}{1-\frac{1}{5}}\] \[=1+3.\frac{1}{5}.\frac{5}{4}\] \[\Rightarrow \] \[\frac{4}{5}S=\frac{7}{4}\] \[\Rightarrow \] \[S=\frac{7}{4}\times \frac{5}{4}=\frac{35}{16}\]
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