# Thread: Question on induction

1. ## Question on induction

I have these 2 questions from my discrete Math assignment and i can't figure out how to deal with it. Inexperienced friends of mine say that the question is wrong. Can anyone help me solve it?

2. Originally Posted by freeze_sr
I have these 2 questions from my discrete Math assignment and i can't figure out how to deal with it. Inexperienced friends of mine say that the question is wrong. Can anyone help me solve it?
Well they both make no sense, the first one should be:

Show that for integers $n\ge 3$:

$2n+1 < 2^n$

RonL

3. Originally Posted by freeze_sr
I have these 2 questions from my discrete Math assignment and i can't figure out how to deal with it. Inexperienced friends of mine say that the question is wrong. Can anyone help me solve it?
hehe, your questions are wrong. the first is not an inequality, it should read $2n + 1 ~{\color{red} < }~2^n$ for $n = 3,4, \dots$. the second question has no real solutions, much less integer solutions.

for the first, here are the steps:

Let $P(n):~2n + 1 < 2^n$ for $n = 3,4, \dots$

Verify that $P(3)$ holds. this is your base case.

Now assume $P(n)$ holds, and show that $P(n + 1)$ holds.

that is, assume $2n + 1 < 2^n$ and show that it implies $2(n + 1) + 1 < 2^{n + 1}$

good luck!

4. Ok thanks.
I'll now have to see my lecturer on these errors.

5. For the second one, I think that the parentheses are meant to be "integer part" symbols:

$\left\lfloor\frac{\lambda^2}4\right\rfloor = \left\lfloor\frac{\lambda-1}2\right\rfloor\, \left\lfloor\frac{\lambda+1}2\right\rfloor$

This is true when λ is an odd integer. In fact, if λ = 2k+1 then both sides are equal to k(k+1).

6. opalg,

Is there a solution for the second question?
Is λ = 2k+1 the final answer?

7. OK, according to my lecturer, the first question is correct.
The question requires me to prove that it is wrong.
The second question had a missing word and should read
" Show that if lambda is an odd integer"
Could you help me out?

8. Originally Posted by freeze_sr
OK, according to my lecturer, the first question is correct.
The question requires me to prove that it is wrong.
The second question had a missing word and should read
" Show that if lambda is an odd integer"
Could you help me out?
Please repost what you think the questions now are.

RonL

9. ## Resolved

Nevermind. It's obvious that these questions have errors. I will have to come up with something.