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
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