Question

what is the alternating sequence of e^-n what is the alternating sequence of e^-n @Mathematics

Answer 1

power series expansion o f
\[e^x\] is
\[\sum_{k=0}^{\infty}\frac{x^k}{k!}\]
replace x by -x to get
\[\sum_{k=0}^{\infty}\frac{(-x)^k}{k!}\]
or if you prefer
\[\sum_{k=0}^{\infty}\frac{(-1)^kx^k}{k!}\]

Answer 2

does that mean its geometric?

Answer 3

no it is not geometric. geometric means there is a common ratio, as in
\[\sum ar^n\]

Answer 4

so the alternating sequence DNE?

Answer 5

?