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For the following G.P.s, find Sn 0.7, 0.07, 0.007, .....

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Question

For the following G.P.s, find Sn

0.7, 0.07, 0.007, .....

Sum
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Solution

a = 0.7 = `7/10`, r = `0.07/0.7 = 1/10 < 1`

Sn = `("a"(1 - "r"^"n"))/(1 - "r")`, for r < 1

= `(7/10[1 - (1/10)^"n"])/(1 - 1/10)`

= `7/9 (1 - 1/10^"n")`

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Chapter 2: Sequences and Series - Exercise 2.2 [Page 31]

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