The value of $$\frac1{0.8} + \frac1{0.08} + \frac1{0.008} + …….$$​Up to the seventh term is__________.

Correct option is D

Given:

​$$\frac{1}{0.8}, \frac{1}{0.08}, \frac{1}{0.008}, \ldots \text{ up to 7 terms}$$​​

Formula Used:

Sum of G.P. = $$a \cdot \frac{r^n - 1}{r - 1}$$ 

where, a = first term, r = common ratio

Solution:

First term: a = $$\frac{1}{0.8}$$​ = 1.25

Common ratio r = $$\frac{\frac{1}{0.08}}{\frac{1}{0.8}} = \frac{12.5}{1.25}$$​= 10

n = 7

Now,

S = $$1.25 \cdot \frac{10^7 - 1}{10 - 1}$$​​

​$$= 1.25 \cdot \frac{10000000 - 1}{9}$$​​

​$$= 1.25 \cdot \frac{9999999}{9}$$​​

​$$= 1.25 \cdot 1111111 = 1388888.75$$​​