Question

{1/1, 1/3, 1/2, 1/4, 1/3, 1/5, 1/4, 1/6}

This is case-defined. One for odd, one for even. It is the odd that I am having trouble with...

Answer 1

the sequence is given by
http://www.wolframalpha.com/input/?i=evaluate+1%2F%281%2F2%281%2F2+%281+%2B+%28-1%29^%281+%2B+n%29%29+%2B+n%29+%2B+%281+%2B+%28-1%29^n%29%29%2C++n%3D1%2C2%2C3%2C4%2C5%2C6%2C7%2C8%2C9%2C10
\[ t_n = \frac{1}{1+(-1)^n+\frac{1}{2} \left(\frac{1}{2} \left(1+(-1)^{1+n}\right)+n\right)} \]