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Question
Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015,…
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Solution
The given G.P. is 0.15, 0.015, 0.00015,...
First term, a = 0.15
Common ratio, r = `0.015/0.15` = 0.1
Sum of geometric series = `("a"(1 - "r"^"n"))/(1 - "r")`
= `(0.15[1 - (0.1)^20])/(1 - (0.1))`
= `(0.15[1 - (0.1)^20])/0.9`
= `(1 - (0.1)^20)/6`
= `1/6[1 - (0.1)^20]`
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