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Question
Find the sum `[("a" - "b")/("a" + "b") + (3"a" - 2"b")/("a" + "b") + (5"a" - 3"b")/("a" + "b") + ... "to" 12 "terms"]`
Solution
= `1/("a" + "b") [("a" - "b") + (3"a" - 2"b") + (5"a" - 3"b") + ... 12 "terms"]`
Here a = `("a" - "b")/("a" + "b"), "d"` = t2 – t1
= `(3"a" - 2"b")/("a" + "b") - ("a" - "b")/("a" + "b")`
d = `(2"a" - "b")/("a" + "b")`
∴ Sn = `"n"/2 (2"a" + ("n" - 1)"d")`
S12 = `12/2[2(("a" - "b")/("a" + "b")) + 11 xx ((2"a" - "b")/("a" + "b"))]`
= `6[(2"a" - 2"b" + 22"a" - 11"b")/("a" + "b")]`
= `6[(24"a" - 13"b")/("a" + "b")]`
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