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Question
For the following G.P.'s, find Sn: p, q, `"q"^2/"p", "q"^3/"p"^2`, ...
Solution
p, q, `"q"^2/"p", "q"^3/"p"^2`, ...
Here, a = p, r = `"q"/"p"`
Let `"q"/"p" < 1`
Sn = `("a"(1 - "r"^"n"))/(1 - "r")`, for r < 1
∴ Sn = `("p"[1 - ("q"/"p")^"n"])/(1 - "q"/"p")`
∴ Sn = `"p"^2/"p - q" [1 - ("q"/"p")^"n"]`
Let `"q"/"p" > 1`
Sn = `("a"("r"^"n" - 1))/("r" 1)`, for r > 1
∴ Sn = `("p"[("q"/"p")^"n" - 1])/("q"/"p" - 1)`
= `"p"^2/"q - p"[("q"/"p")^"n" - 1]`
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