Induction inequalities (1 Viewer)

[Joshmosh2]

For proving inequalities by induction, at what point can you finally say that the statement is true?

For example, for the question
1 + 1/2 + 1/3 + ... + 1/n < √(n), for n >= 7

I proved true for n = 7,
then assumed n = k

but for proving true for n = k+1, what exactly do I have to do?
Wouldn't subbing into the initial result give you the right answer?
Why do we usually simplify the expression and then make the statement?

Thanks in advance