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Question
Find the sum of G.P. :
`1 - 1/2 + 1/4 - 1/8 + ..........` to 9 terms.
Solution
Given G.P. : `1 - 1/2 + 1/4 - 1/8 + ..........`
Here,
First term, a = 1
Common ratio, r = `(-1/2)/1 = -1/2` ...(∵ r < 1)
Number of terms to be added, n = 9
∴ `S_n = (a(1 - r^n))/(1 - r)`
`=> S_8 = (1(1 - (-1/2)^9))/(1 - (-1/2))`
= `(1 - (-1/2)^9)/(1 + 1/2)`
= `(1 + 1/2^9)/(3/2)`
= `2/3(1 + 1/2^9)`
= `2/3(1 + 1/512)`
= `2/3 xx 513/512`
= `171/256`
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