Series/logarithm questions

Hi, I was wondering how to solve these 2 questions:

c) use the proof from part a) and d) [e^x=>x+1 and (1+1)(1+1/2)...(1+1/n)=n+1] to prove that e^(1+1/2+1/3+...+1/n)>n

d) Find a value of n for which 1+1/2+1/3+...+1/n>100

You don't have to provide the entire answer, but some hints or part of the work would be nice.

Thanks in advance!

Re: Series/logarithm questions

Having established that:

and:

we may write:

Since all values are positive, we may multiply down. What do you get?

d) Having established that:

this implies:

Now, let:

What does this say about ?

Re: Series/logarithm questions

Oh...thanks so much. I can't believe I didn't think that way for c) :( disappointed in myself lol