Question

Find the sum:

`(a - b)/(a + b) + (3a - 2b)/(a + b) + (5a - 3b)/(a + b) +` ... to 11 terms

Answer 1

Here, first term (A) = `(a - b)/(a + b)`

And common difference,

D = `(3a - 2b)/(a + b) - (a - b)/(a + b)`

= `(2a - b)/(a + b)`

∵ Sum of n terms of an AP,

S_n = `n/2[2a + (n - 1)d]`

⇒ S_n = `n/2{2((a - b))/((a + b)) + (n - 1) ((2a - b))/((a + b))}`

= `n/2{(2a - 2b + 2an - 2a - bn + b)/(a + b)}`

= `n/2((2an - bn - b)/(a + b))`

∴ S₁₁ = `11/2{(2a(11) - b(11) - b)/(a + b)}`

= `11/2((22a - 12b)/(a + b))`

= `(11(11a - 6b))/(a + b)`