Exploring Patterns in Mathematical Series and Sequences

[real analyst]

Homework Statement

I need to find three mathematical series, for the following patterns

1) Sn= 1/n if n is odd, or 1 of n is even.

2) Sn= 0,1,0,.5,1,0,1/3,2/3,0,1/4...

3) Find a sequence (Sk) which is a subset of the natural numbers in which every positive integer appears infinitely many times...that is, for each n in the Natural numbers, Sk=n for infinately many k's. any ideas?

Homework Equations

I guess they're arent any relevant equations to these. I guess yuo just have to get the pattern

The Attempt at a Solution

well, I know the first two are similar and that's about all I know. they're not p-series, geometric, alternating, or anything like that so I'm kind of stuck

The third one, well, I don't even kow what it means honestly, so can you at least give me a hint?? thanks.

 

[foxjwill]

For 1), try thinking along the lines of

$$(-1)^n = \begin{cases} -1 & n\mbox{ is odd}\\ 1 & n\mbox{ is even} \end{cases}$$

For 2), try thinking along the lines of the periodicity of $$\sin(x)$$.

For 3), I'll have to refer you to the Wikipedia article on "[URL Paradox[/URL].