Question

Find the sum of 7 terms of the series 2 + 0.2 + 0.02 + ....

Answer 1

a = 2

r = `0.2/2`

= 0.1 < 1

`S_n = (a(1 - r^n))/(1 - r)`

`S_7 = (2(1 - (0.1)^7))/(1 - (0.1))`

`S_7 = (2(1 - 0.1^7))/(0.9)`

= `(2 xx 10)/9(1 - (1/10)^7)`

= `20/9(1 - (1/10)^7)`