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Question
Find the sum of G.P. :
0.3 + 0.03 + 0.003 + 0.0003 + ........... to 8 items.
Solution
Given G.P. : 0.3 + 0.03 + 0.003 + 0.003 + ...........
Here,
First term, a = 0.3
Common ratio, r = `0.03/0.3`= 0.1 ...(∵ r < 1)
Number of terms to be added, n = 8
∴ `S_n = (a(1 - r^n))/(1 - r)`
`=> S_8 = (0.3(1-(0.1)^8))/(1-0.1)`
= `(0.3(1 - (0.1)^8))/0.9`
=`(1 - (0.1)^8)/3`
= `1/3(1 - 1/10^8)`
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