Question

Find the limit as n approaches infinity of (1+ 2/n) ^ (1/n)

Answer 1

I know it is 1 but I am not sure how to show it...?

Answer 2

make a guess i bet you are right

Answer 3

Does it equal one just because any number to the power of 0 to 1?

Answer 4

is not to*

Answer 5

Is there any way I can show my work?

Answer 6

oh no, it is definitely not one

Answer 7

Howw?

Answer 8

ok you win it is one
i read it wrong q

Answer 9

Nah it's good, how can I show this work though?

Answer 10

take the log to get the variable out of the exponent and start with
\[\frac{1}{n}\ln(1+\frac{2}{n})\]

Answer 11

Lhospitals?

Answer 12

take the limit of that one, you will get \(0\) so your answer is \(e^0=1\)

Answer 13

yeah you can do it using l'hopital

Answer 14

how did you get the e^0 part?

Answer 15

oh I got it. thanks

Answer 16

because the first step was taking the log

Answer 17

yw