Question

How do you get a formula of the nth term for this sequence:1, 1/2, 3, 1/4, 5, 1/6...?

Answer 1

One possibility is
`color(white)("XXX")a_n = n^((-1)^(n-1))`

Explanation:

The sequence `1, 2, 3, 4,5, 6, ...` is clearly just `a_n = n`
but we want the reciprocal of all even numbered terms and one way to do this is to use the alternating nature of
`color(white)("XXX")(-1)^(n-1)`
(noting that we need to subtract `1` from the exponent `n` so that it is the even and not the odd terms for which we take the recipocal.)