 My Math Forum Help me prove something very easy! [Mathematical Induction]
 User Name Remember Me? Password

 Algebra Pre-Algebra and Basic Algebra Math Forum

 September 24th, 2010, 09:58 AM #1 Newbie   Joined: Sep 2010 Posts: 24 Thanks: 0 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! September 24th, 2010, 11:05 AM #2 Global Moderator   Joined: Nov 2009 From: Northwest Arkansas Posts: 2,767 Thanks: 5 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? September 24th, 2010, 12:18 PM #3 Newbie   Joined: Sep 2010 Posts: 24 Thanks: 0 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.. September 24th, 2010, 05:22 PM #4 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs 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. September 24th, 2010, 07:12 PM #5 Senior Member   Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs 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 September 24th, 2010, 08:31 PM   #6
Global Moderator

Joined: Dec 2006

Posts: 21,027
Thanks: 2258

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. Tags easy, induction, mathematical, prove Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post hs_pec Algebra 1 January 16th, 2013 06:28 PM Phatossi Algebra 4 November 10th, 2012 05:27 PM landonjones6 Calculus 2 September 13th, 2011 12:05 AM BackY Calculus 5 December 31st, 1969 04:00 PM hs_pec Calculus 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top      