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September 24th, 2010, 09:58 AM   #1
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Help me prove something very easy! [Mathematical Induction]

Hey guys.. I'm new to MATH INDUCTION, so I wanted to ask you, to help me prove
2^n (greater than, or equal to) n^2 (where n is GREATER THAN or EQUAL to 4)


I need DETAILED EXPLANATION pleaseeee
I'm new, and I'm trying to do some problems, so I can get comfortable with it!
Thank you!
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September 24th, 2010, 11:05 AM   #2
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Re: Help me prove something very easy! [Mathematical Induct

Let's call the statement P.
You are trying to show that P(n) is true for all n>=4.
Show that it is true for n = 4.
Show that if it is true for a number, then it is true for the next number.

2^4=4^2, so P(4) is true.
Assume P(n). Now the work is to show that P(n+1) is true.


Have you done some simpler induction proofs, like 1+2+3+...+n = n(n+1)/2?
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September 24th, 2010, 12:18 PM   #3
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Re: Help me prove something very easy! [Mathematical Induct

Yeah yeah, I can do that without problem now.. I tried it many times! Now I fully understand that example!
As for one I asked, I got to the n=k+1 step..
Now I can't seem to work them out, and get the form that I want them to be!
I need some algebra there, some creativity.. that's why I'm trying to teach!
If there are more simple problems like that, I'd like to know please! I'm searching for them all week long..
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September 24th, 2010, 05:22 PM   #4
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Re: Help me prove something very easy! [Mathematical Induct

2^n has to have 2^n added to it to get 2^(n + 1) while n^2 only has to have 2n + 1 added to get (n + 1)^2.
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September 24th, 2010, 07:12 PM   #5
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Re: Help me prove something very easy! [Mathematical Induct

2^n may be written as (1 + 1)^n = nCr(n,0) + nCr(n,1) + ... + nCr(n,n-1) + nCr(n,n)

When n ? 4 we have 2^n = 2n + 2 + [nCr(n,2) + ... + nCr(n,n-2)] (at least one term in the brackets)

It is easy to see that

2n + 2 + [nCr(n,2) + ... + nCr(n,n-2)] ? 2n + 1

1 + [nCr(n,2) + ... + nCr(n,n-2)] ? 0
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September 24th, 2010, 08:31 PM   #6
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Quote:
Originally Posted by BackY
I'm new to MATH INDUCTION!
Welcome. Your topic is not about calculus, so I've moved it to where it should have been posted.

Also, you should have been able to post your attempt to solve the problem before asking for help. There are numerous textbooks (some online) that explain how to use mathematical induction and give examples of its use.
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