Visualizing Limits with Factorials and Powers

[sedaw]

how to calculate the limits ?

appreciate any kind of help ...

 

[sedaw]

n!/n^n

2^n/n!

n!/2^n

1/n + [1 + (-1)^n] / [2^(1/n)]

 

[VeeEight]

You should show that you have done a little work on the problems.

Here is a hint to visualize some of the limits. n! is the product of n terms, one of them is n and the rest are all less than n. n^n is the product of n terms, all of them are n.