( 5 months ago )
The sequence is f=0,1,0,1,…
I want to find a general formula for the nth element. The sequence starts at n=0 (the 0 here is not the first element 0 but rather denotes the 0th position).
One easy and obvious solution is: nth f=nmod2. This works because even positions have 0 and odd positions have 1.
However, this question is part of a homework and modulus has not been discussed (or part of the syllabus or even a prerequisite). And so I am hesitant to use it.
Is there another way to solve this problem using only basic arithmetic operations (one that a beginning high schooler knows of)?