The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, .. , is

Options

A. ` 7/18(179-10^(-20))`
B. ` 7/9(99-10^(20))`
C. ` 7/81 (179+ 10^(-20))`
D. ` 7/9(99+10^(-20))`

Answer

c

Explanation

` S = 7/10 + 77/(10^(2)) +777/(10^(3)) +….+ ` upto 20 terms
` =7/9 [ 9/10 + 99/100+999/1000+...+" upto 20 terms"]`
` 7/9 [ (1-1/10)+(1-1/(10^(2)))+(1-1/(10^(3)))+...+" upto 20 terms"]`
` = 7/9 [ (1+1+….+ " upto 20 terms" )-(1/10 +1/(10^(2))+1/(10^(3))+....+" upto 20 terms ")]`
`= 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)]`