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Question
Find the sum of the following series to infinity:
10 − 9 + 8.1 − 7.29 + ... ∞
Solution
This infinite G.P has first term a = 10 and common ratio r = `-9/10 = -0.9`
Thus the sum of the infinite G.P will be:
10 - 9 + 8.9 - 7.29 + ... ∞ = `"a"/(1-"r")` [Since |r| < 1]
= `10/(1-(-0.9))`
= `10/1.9`
= `100/19`
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