I need help.

[macdude425]

I have a pre-calculus exam Wednesday/Thursday. I'm ready, save for one part - I don't know how to do mathematical induction.

Here's an example problem.

3+6+9...(summation notation, k=1, n=10)3n=3n/2*(n+1); prove by induction the statement is true.

I can get the first part (show that both are true when n=1) but I always screw up the second part (show that both are true when n=(k+1)).

Help, please. Thanks.

 

[peterhuang913]

i am 16, in precalc, and learning this this week. Its fresh in my mind, whats the original equation?
heres the equation example of my worksheet, it requires sum of a sequence:

eaxmple: Sn=1+3+5+7+9+...+2k-1=n^2
1) S1=1=1^2
2) Suppose Sk=1+3+5+7+...+2k-1=k^2
      replace n with k, a variable for any number
    Prove S(k+1)=1+3+5+7+...+(2k-1)+2(k+1)-1=(k+1)^2
      since the number after 2k-1 is 2(k+1)-1, we add it after the sequence, also to k^2
3) 1+3+5+7+...+2k-1+2k+2-1=k^2+2k-1 :simplify
                        Sk+2k+2-1=
                         k^2+2k+1=k^2+2k+1
4) Since k and k+1 is true, we can assume all numbers to be true

 

[macdude425]

We were given no equation for doing these types of problems - just told to do two things:
1. Prove the statement is true for n=1
2. Prove the statement is true for n=K+1.

However, I do believe I have caught my mistake - there are three statements equal to each other - I forgot to let n=K+1 in one of them. I'm going to check to make sure that's what it was.

Thanks.

 

[peterhuang913]

n=1 is step 1
n=k+1 is step 2.5

 

[macdude425]

Yeah - I don't understand why we suppose the set n=k step, but mine is not to reason why, I suppose.

 

[Oreo]

I hope i never have to learn this.

 

[Ethereal_Dragon]

k=(k+1)

I did Trig my senior year in HS, then somehow managed to enroll in an HONORS Pre-calc class my first class in College..... I never made it that far....

Tell me though... was that a typo, (perhaps you meant n=k+1), cause I think my brian just melted...

 

[macdude425]

Yes, I typo'ed. Please excuse me - I just changed it.

 

[Trotter]

It has been WAY too long since I did this stuff. I remember doing it back in the day... when I wasn't too busy checking out the other figures sitting nearby. Man, there were a lot of brainy babes back then...

 

[Mr. Switch]

psht,

calc is for n00bs