Question

How do you find general term formula for {-1/4, 2/9, -3/16, 4/25, ...}?

Answer 1

`n^(th)` term of the series `{-1/4, 2/9, -3/16, 4/25, ...}` is`((-1)^nxxn)/(n+1)^2`

Explanation:

Here one desires is the `n^(th)` term of the series `{-1/4, 2/9, -3/16, 4/25, ...}`.

As is observed the numerators are `{-1, 2, -3, 4, ...}`. Hence numerator of `n^(th)` term is `n` if `n` is odd and `-n` if `n` is even.

Hence we can write numerator of `n^(th)` term as `(-1)^nxxn`.

The denominators are `{4,9,16,25,...}` i.e. `n^(th)` term is the square of `(n+1)` or `(n+1)^2`.

Hence general formula for `n^(th)` term of the series `{-1/4, 2/9, -3/16, 4/25, ...}` is `((-1)^nxxn)/(n+1)^2`