Question

Converge to what?

( 1 + ( 1/n ) )^2n

Answer 1

I know the answer is e^2.. but I was hoping someone can show how. I tried the ratio test, but got it wrong!

Answer 2

\[e^{ \lim_{x \rightarrow \infty}( 1 + ( 1/n ) )^2n } \]

Answer 3

sorry the n is an exponent as well

Answer 4

Hello, thanks for answering! Why is it that we raise the exponent here with e?

Answer 5

than you drop the 2 so it becomes e^2(the limit)

Answer 6

usually when we have exponents and we don't know how to solve the type of equation using a method we already know, we resort to using e to drop the exponent

Answer 7

What technique is that? Haven't come across it yet in my studies

Answer 8

the limit changed to 2n log (1+1/n) btw

Answer 9

I learnt it in highschool calculus, i dont remember which section exactly though

Answer 10

okay i'll do some researching then. Thanks! problem solved

Answer 11

your welcome :)