Question

limit (1+1/n)^n as n approaches infinity

Answer 1

I keep on getting 1, but I do not think that is the answer.

Answer 2

Check this out, there is a direct formula for evaluating this type of limit.
http://www.mathsisfun.com/calculus/limits-infinity.html

Answer 3

And you're right 1 is not the answer

Answer 4

@LucyLu15 Do you follow?

Answer 5

I see...but it's the steps that confuse me.

Answer 6

its an indeterminate of the form 1^infinity. so we must use L'Hopitals rule. replace n with x and set the function equal to y. take the natural log of each side (ln). You then get the form infinity x infinity. because you move the exponent down to a multiplying coefficient. then reshape the equation so it is in the form 0/0. use L'hopitals rule by taking the derivative of each function separately and u get 1/(1+(1/x)) which equals 1 when you take the limit as x approaches infinity. now you have lny =1. take the e of both sides and the final answer is e