I don't understand how you get this limit to equal this.
#Finding this limit
cursive nacelle
sour elkBOT
I don't understand how you get this limit to equal this.
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livid olive
exp(-n log(1+1/n))
carmine needle
(n +1)^n / n^n = (1 + 1/n)^n
Which is known to converge to exp(1)
Otherwise known as e
Then what does n^n / (n +1)^n converge to?
runic terrace
1/e
carmine needle
In general, it is good to know that for a fixed x in R, (1 + x/n)^n converges to exp(x) as n goes to infinity
cursive nacelle
sorry went for dinner
cursive nacelle
(n +1)^n / n^n = (1 + 1/n)^n
how do you get the reciprocal here?
carmine needle
No I just started from it for convenience
if $a_n$ goes to $l \neq 0$, then $\frac{1}{a_n}$ goes to $\frac{1}{l}$ yeah?
swift capeBOT
Rion
west galeBOT
@cursive nacelle has given 1 rep to @carmine needle
cursive nacelle
+close