What is the value of $$\frac{1}{{0.2}} + \frac{1}{{0.02}} + \frac{1}{{0.002}} + \,.....$$     upto 9 terms?

Solution (By Examveda Team)

$$\eqalign{ & \frac{1}{{0.2}} + \frac{1}{{0.02}} + \frac{1}{{0.002}} + \,.....\,{9^{{\text{th}}}}{\text{ term}} \cr & {\text{ = }}\frac{1}{2}\left[ {10 + 100 + 1000 + \,.....\,{9^{{\text{th}}}}{\text{ term}}} \right] \cr & = \frac{1}{2}\left[ {1111111110} \right] \cr & = 555555555 \cr} $$