Question

Find the sum: `4 - 1/n + 4 - 2/n + 4 - 3/n + ...` upto n terms

Answer 1

Here, first term, `a = 4 - 1/n`

Common difference,

`d = (4 - 2/n) - (4 - 1/n)`

= `(-2)/n + 1/n`

= `(-1)/n`

∵ Sum of n terms of an AP,

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

⇒ `S_n = n/2[2(4 - 1/n) + (n - 1)((-1)/n)]`

= `n/2 {8 - 2/n - 1 + 1/n}`

= `n/2(7 - 1/n)`

= `n/2 xx ((7n - 1)/n)`

= `(7n - 1)/2`