Question

Find the sum `[("a" - "b")/("a" + "b") + (3"a" - 2"b")/("a" +  "b") + (5"a" - 3"b")/("a" + "b") + ...  "to"  12  "terms"]`

Answer 1

= `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")`

∴ S_n = `"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")]`