Question

Why are these summations the same?

Answer 1

\[\sum_{k=-\infty}^{0} e^{|k|} = \sum_{k=0}^{\infty} e^{-k}\]

Answer 2

because if \(k<0\) then \(|k|=-k\)

Answer 3

Oh I see what you mean, so if it's k>0 then would rewriting it in the second form be in the same terms, k=0 to infinity?

Answer 4

I mean like if k>0 could I rewrite as

\[\sum_{k=0}^{\infty} e^{k}\]

Answer 5

for the second form? Just want ot make sure I understand this