श्रेढी 0.7, 0.77, 0.777......, के प्रथम 20 पदों का योग है|

Options

A. `7/81(179-10^(20))`
B. `7/9(99-10^(-20))`
C. `7/81(179 + 10^(-20))`
D. `7/9(99 + 10^(-20))`

Answer

C

Explanation

`7/10 + 77/100 + 777/10^(3) +........... + 20` पदों तक
`= 7[1/10 + 11/100 + 111/10^(3) + 20]`
`7/9[(1-1/10) + (1-1/10^(2)) + (1-110^(3)) + ....20]`
`=7/9[20 - (1/10(1-(1/10)^(20)))/(1-1/10)] = 7/9[20-1/9(1-(1/10))^(20)]`
`=7/9[179/9 + 1/9(1/10)^(20)] = 7/81[179 + (10)^(-20)]`