Posted by Frederick E. on .
Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x>0...
Should i use the formula e= lim as x->0 (1+x)^(1/x)
e= lim as x->infinity (1+1/n)^n
Am i able to substitute in x/n for x? and then say that
e lim x ->0 (1+x/n)^(1/(x/n))
and then raise it to the xth power
ie. e^x and lim x -> (1+x/n)^(n)
Thanks for any help.. just tell me if is correct please or if i am on the right track
also,, how do i say that this is for all x>0?