Remember that when we work with limits the inequalities situations has a different behavior. It's possible having a convergent sequence x_n with every term greater than a ( a is a real number) and its limit is equal or greater than a. Example : The sequence 1/n is strictly positive, although its limits is equal to 0
Neat
You can also pretty easily prove this by letting N > -x, and seeing that for all n > N, 1+x/n > 0, meaning that the limit of (1+x/n)^n > 0.
Remember that when we work with limits the inequalities situations has a different behavior. It's possible having a convergent sequence x_n with every term greater than a ( a is a real number) and its limit is equal or greater than a.
Example : The sequence 1/n is strictly positive, although its limits is equal to 0
e^x > 0, and then moment generating functions go brrrr
consider covering some proofs from probability or statistical inference at some point