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Question
Find the sum to indicated number of terms in the geometric progressions 1, – a, a2, – a3, ... n terms (if a ≠ – 1).
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Solution
Geometric progressions 1, –a, a2, –a3, …
First term, a1 = 1, common ratio, r = `(-a)/1 = -a`
∴ Sum of n terms (Sn) = `(a_1(1 - r^n))/(1 - r)`, r > 1
= `(a(-a)^n)/(1 - r)`, r > 1
= `(1.[1 - (-a)^n])/(1 -(-a))`
= `([1 - (-a)^n])/(1 + a)`
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