- #1
Xcron
- 22
- 0
Ok, the problem says:
Show that [tex]\lim_{n\rightarrow\infty} (1+\frac{x}{n})^n = e^x[/tex] for any [tex]x>0[/tex].I thought that I could say that y = 1+x/n...and then use the natural logarithm to narrow it down to [tex]\ln y=n\ln(\frac{x}{n})[/tex] ... I should be getting [tex]x[/tex] so that when I take it back into the original limit, I would have [tex]e^x[/tex] but I can't seem to make it that way..
Show that [tex]\lim_{n\rightarrow\infty} (1+\frac{x}{n})^n = e^x[/tex] for any [tex]x>0[/tex].I thought that I could say that y = 1+x/n...and then use the natural logarithm to narrow it down to [tex]\ln y=n\ln(\frac{x}{n})[/tex] ... I should be getting [tex]x[/tex] so that when I take it back into the original limit, I would have [tex]e^x[/tex] but I can't seem to make it that way..