Question

what is exact limit ?​

Answer 1

Answer:

We can start from the limit:

limx→∞(1+1x)x=e

Consider now:

limx→∞(1+3x)x

and substitute x=3y to have:

limx→∞(1+3x)x=limy→∞(1+33y)3y=limy→∞((1+1y)y)3=e3

Then the sequence we obtain in the particular case where y=n converges to the same limit.