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

1 Answer
Nov 12, 2015

Answer:

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.)