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प्रश्न
Find the sum to indicated number of terms in the geometric progressions 1, – a, a2, – a3, ... n terms (if a ≠ – 1).
उत्तर
geometric progressions 1, –a, a2, –a3,…
First term, a = 1, common ratio, r = `(-"a")/1 = -"a"`
∴ Sum of n terms = `("a"(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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