What would be the formula for the sequence An, for...

0, 2, 0, 2, ...
1/2, 1/5, 1/10, 1/17, ...

Question

What would be the formula for the sequence An, for...

0, 2, 0, 2, ...
1/2, 1/5, 1/10, 1/17, ...

precal · Answer

0,2,0,2,......
I do not believe has a formula.
We tend to write formulas if the sequence is arithmetic or geometric.

precal · Answer

I could be wrong on that,  hopefully someone can give you a formula.

rogue · Answer

Do you know the equation for the second one though? I'm pretty sure its recursive.

rogue · Answer

Here are the answers if you still want to know.
$$\left\{ 1 + (-1)^n \right\}_{n = 1}^{\infty} = 0, 2,0,2,0,...$$$$\left\{ \frac {1}{n^2 + 1} \right\}_{n = 1}^{\infty} = \frac {1}{2}, \frac {1}{5}, \frac {1}{10},...$$

precal · Answer

yeah, I believe it.  Students do have a hard time coming up with those solutions unless they have a lot of experience with series and sequences.

rogue · Answer

We were just being given our introduction to infinite series that day. This stuff is pretty easy now =)

precal · Answer

calculus?

rogue · Answer

Yeah, BC Calc =)