1. ## Induction help needed please

Define the sequence (L_n) by
L_n=1/(n+1)+1/(n+2)+1/(n+3)+ … + 1/2n for n ≥1

Show using an inductive or non-inductive argument that

L_(n +1)=L_n + [1/((2n +1)(2n +2))] for n ≥1

and

L_n<n(1/(n +1)) for n ≥2

Many thanks.

2. Originally Posted by alpha
Show using an inductive or non-inductive argument that

L_(n +1)=L_n + [1/((2n +1)(2n +2))] for n ≥1

Many thanks.
You do realize you did not even say what $L_n$ is, right?! The logical assumption is that they are the Lucas numbers. But, this doesn't seem to be true then.

3. Sorry for the mistake. I just corrected the question.

Thanks.

4. Originally Posted by alpha
Define the sequence (L_n) by
L_n=1/(n+1)+1/(n+2)+1/(n+3)+ … + 1/2n for n ≥1

Show using an inductive or non-inductive argument that

L_(n +1)=L_n + [1/((2n +1)(2n +2))] for n ≥1

and

L_n<n(1/(n +1)) for n ≥2

Many thanks.
Hint: $L_n=H_{2n}-H_n$ where $H_n$ is the n-th harmonic number. That should make things easier.

6. Originally Posted by alpha
It would help you more if you did at least some of it and reported back with any problems.

7. Sorry but the whole problem is that I cant do this question at all.

8. Originally Posted by alpha
Sorry but the whole problem is that I cant do this question at all.
What's induction?

9. i dont know

10. Originally Posted by alpha
i dont know
Are you serious? Why would you be given a problem you aren't equipped to solve.

Mathematical induction - Wikipedia, the free encyclopedia