Find common term for this sequence

[NihalRi]

Homework Statement

6 /(12 + 1), 1/(22 + 1),6/(32 + 1),1/(42 + 1)

Homework Equations

none

The Attempt at a Solution

I suspect this is not that hard, I get the denominators but the numerator alternates so I though I would need 6 to be the base of a power that alternates between 0 and 1 but I can't think of anything :/

 

[andrewkirk]

Are you trying to find a formula for the nth term in the sequence?

You can handle the alternation between 1 and 6 by using the mod function, expressing things in mod 2.

Or, there's a special number that, when raised to the power of integer $n$, gives alternating behavior of the type you seek. What number is that?

 

[NihalRi]

Are you trying to find a formula for the nth term in the sequence?

You can handle the alternation between 1 and 6 by using the mod function, expressing things in mod 2.

Or, there's a special number that, when raised to the power of integer $n$, gives alternating behavior of the type you seek. What number is that?

yes that's what I'm trying to do
I've never heard of a mod function:/ but i'll google it. A number that alternates between one and zero? can't think of one, hint?

 

[andrewkirk]

A number that alternates between one and zero?

The number doesn't alternate. Its powers do ('power' as in multiplying a number by itself an integer number of times). Every time we increase the power/index/exponent by 1, the result switches from one of the possible values to the other. Also, the two possible values are not 1 and 0.

The link for mod function is a hyperlink in my post above (blue text).