Here is the problem:
You have n-steps to climb. You can only climb 1 or 2 steps at a time. find the number of ways to reach Nth step.
the solution is described as t(n) = t(n-1) + t(n-2).
I keep thinking why not add a constant 2, to represent the final one or two step from t(n-1) and t(n-2)? I having trouble intuitively, why it's not added at each stage?
the problem is the sum of t(n-1) and t(n-2) but I feel like where does it account for taking the one or two step backwards?
since there are two option and you have yet to take the two steps at t(n-1) or t(n-2) shouldn't there be a constant added at each step? How can I conceptualize this?
and you have yet to take the two steps
But you're not counting steps though, you're counting ways. Your final step/jump can be a one or a two. So you add the number of ways that led you to n-1 with the number of ways that led you to n-2. That's your answer.