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

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The discussion focuses on creating a series where the term a_n equals 1 for odd n and 2 for even n. Several mathematical expressions are proposed to achieve this pattern, including a_n = 2 - n mod(2) and a_n = 2 - [sin^2(πn/2)]. Another suggested formula is a_n = (3 + (-1)^n) / 2, which also meets the criteria. The conversation highlights both discrete and continuous approaches to defining the series. Overall, the participants share various methods to represent the alternating series effectively.
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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
 
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Can anyone help me come up with some a_n such that this is true?
 
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
 
There is also ##\frac{3+(-1)^n}{2}##
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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