Series of sorts- Return 1 or 2 based on even or odd n

[connordurkin]

I would like to create a series where for each term if n is odd the term =1 and if n is even, the term = 2. I.e.

$a_{n} = 1 if \ n \ is \ odd \ and \ a_{n} = 2 \ if \ n \ is \ even$

 

[connordurkin]

Can anyone help me come up with some a_n such that this is true?

 

[Gackhammer]

So what you are saying is ...

For input n = 1,2,3,4,5...

a_n = 1,2,1,2,1,2There are a number of ways you can do this (click on Equations for Links )...

$2- n mod(2)$

$2-[sin^2(\frac{\pi n}{2})]$Just a couple that I thought off in my head...
One is discrete, one is continuous

 

[pwsnafu]

There is also $\frac{3+(-1)^n}{2}$

 

[CellCoree]

This series is known as the "alternating series" or "alternating sequence" and can be represented by the mathematical notation a_{n} = (-1)^{n+1}. This notation indicates that the term will alternate between positive and negative values, with odd terms being positive (1) and even terms being negative (-1). This type of series has been studied extensively in mathematics and has many interesting properties and applications. It is an important concept in calculus, where it is used to test for convergence of infinite series. In scientific research, this type of series can also be used to model real-world phenomena that exhibit alternating patterns or behaviors. Overall, the alternating series is a valuable tool in mathematics and can be applied in a variety of contexts.