Find the sum to indicated number of terms in each of the geometric progressions : 0.15, 0.015, 0.0015, . . . , 20 terms.

Answer

N/a

Explanation

Given G.P. : 0.15, 0.015, 0.0015,…
`"1st term "a_(1)=a=0.15`
`"2nd term "a_(2)=0.015`
` therefore" Common ratio "r=(a_(2))/(a_(1))=(0.015)/(0.15)=0.1=(10)^(-1)`
`because" Sum of n terms of G.P."`
`S_(n)=(a(1-r^(n))/(1-r)" "(rlt1)`
`rArr" "S_(20)=(0.15[(1-(0.1)^(20))])/((1-0.1))`
`rArr" "S_(20)=(0.15[1-(0.1)^(20)])/((0.9))=(1)/(6)[1-(0.1)^(20)]`
`therefore"Sum of 20 terms "=(1)/(6)[(1-(0.1)^(20))]`