- #1

nathangeo

- 4

- 0

You could break down the sum into: (t^(n))*e + (t^(n-1))*e + (t^(n-1))*e + ... + (t^(n-n))*e ; where e = e^(-st)

To evaluate this, notice that all terms will go to zero when evaluated at infinity

However, when evaluated at zero, notice the last term of the summation; when i=n : (t^(0))*e^(-st)

(t^0) is equivalent to one so we could rewrite as (1). When evaluating the last term at zero, then, we obtain (1) from the e^(-st) term. But, if you think of (1) as t^0, evaluating the last term at zero will give you 0^0, or which cannot be evaluated.

My question is, how do we handle a situation like this? I can change (t^0) to (1) and then evaluate the bounds; or leave it as it is (t^0), and find that evaluating the bound at zero creates an indeterminant value.