Anyone taking discrete math or know how to do math induction???

[Armageddon415]

Need some help on two of my hw q's.
Question 1
Question 2

Been stuck on these for a while and would be grateful if someone helped me on them.

 

[bolomite]

aargh, proofs! Wish I could help ya

 

[Armageddon415]

yep, hated these in high school, hate them now in college

 

[VBboy]

I loved this sh|t Maybe I will help you later on

 

[thraashman]

took discrete math, passed it even, still don't know how to do induction. sorry, that stuff's a real pain in the ass. good luck

 

[Armageddon415]

please help, i hate this sh!t

 

[Sahakiel]

Hm... induction... let's see how much I remember...

First step: Prove the claim is valid for P(1).
Second step : Assume P(k) is true given P(1) is true.
Third step : Prove P(k+1) is true for all k.

The first question is pretty easy.
As for the second question, well, I'm having trouble thinking beyond proof by cases. Unless you can think of anothe way, then you're looking at one very long proof.

 

[VBboy]

Or you could use the formula for geometric series, if applicable
http://www.mathsyear2000.org/alevel/pure/purtutsergeo.htm

 

[gopunk]

for question 1, you can simplify it down to just having to show that

1/n + 1/(n + 1)^2 > 1/(n+1)

which you can do by subtracting 1/n from both sides... the right side will turn into a negative number, and it's cake from there.



as for the second.... what about n = 9, k = 8, m = 9?

 

[VBboy]

I'm too sleepy. But this is directly related to the proof of "1/2 + 1/4 + 1/8 + ... < 1/2". Try to find it, it's a basic proof. "Will a frog whose each next jump is twice as short as the previous one reach the end of the tunnel" type of thing.

Googel rox

The Sum of the Geometric Series 1 + 1/2 + 1/4 + ...

 

[Armageddon415]

bump for help on the second one. Got the first one after a while.