Question

I have two excercises that I'm proving with math induction. I'm confused.

Answer 1

In both we have that n needs to be bigger or equal 2.

So why do we in the first excercise only need one member and in the second excercise 2 members?

In both cases n = 2.

Correction: in g) last member is 2n.

Answer 2

For g), your induction start is correct. For the induction step, going from n to n+1, there is a large amount of overlap between the sums. We *exclude* the term 1/(n + 1) because we start at 1/((n+1) + 1), but we include the terms 1/(2n+1) and 1/(2n+2). Since we can use the induction hypothesis in our proof we only have to show that we're adding more than we're taking away, i.e. if the sum for n is bigger than 1/2 and going to n+1 increases the value, then the new sum is also going to be bigger than 1/2.

Answer 3

It’s continuous, you can’t take only the first two values.