- #1
rustyjoker
- 5
- 0
Homework Statement
Big problem with exponential function proof assignment, need some help.
let
x≥0 and for every k[itex]\in N[/itex] there is [itex]n_{k}[/itex][itex]\in N[/itex] and
[itex]x_{k1}[/itex]≥...≥[itex]x_{k_{nk}}[/itex] and [itex]x_{k1}[/itex]+...+[itex]x_{k_{nk}}[/itex]=x.
Proof: if [itex]lim_{k→}∞ x_{k1}[/itex]=0 then [itex]lim_{k→}∞
[/itex] (1+[itex]x_{k1}[/itex])·...·(1+[itex]x_{k_{nk}}[/itex])=exp(x)=[itex]e^{x}[/itex]