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March 29, 2024, 11:50:36 pm

Author Topic: 3U Maths Question Thread: Ask Your Questions Here!  (Read 1728 times)  Share 

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jamonwindeyer

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3U Maths Question Thread: Ask Your Questions Here!
« on: June 17, 2015, 08:47:01 pm »
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Hey everyone! It would be awesome to have a place to collaborate and help each other out on tricky problems, we have a community full of brainiacs. So here is that space! Have at it! Ask any questions you have on your mind below. I'll do the rounds once a day, and if it is a question which I feel should be shown to lots of people, I'll even start a new thread for it to share the knowledge  ;D ;D ;D
« Last Edit: June 17, 2015, 09:31:43 pm by Ned Nerb »

hsceebz

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Re: 3U Maths Question Thread: Ask Your Questions Here!
« Reply #1 on: June 19, 2015, 02:57:49 pm »
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if someone could help with this induction question that would be much appreciated

jamonwindeyer

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Re: 3U Maths Question Thread: Ask Your Questions Here!
« Reply #2 on: June 20, 2015, 11:15:15 am »
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if someone could help with this induction question that would be much appreciated
(Image removed from quote.)

Hey again! Okay, I can help with this one. So the prove by induction, we use three steps:

Step 1: We prove for the lowest integer value we need to satisfy the condition (in this case, 1). So we just sub that in and check if it is divisible by three, which it is.

Step 2: We assume that the condition is true for , where k is some integer which meets our conditions. This just sets up a general case, which hasn't been proven yet. We let this condition be:



Such that is some integer. This is how we denote divisibility in all induction questions.

We now test for . Now there are several ways to proceed, but I think the easiest to understand is immediately bring the previous line into the expression, we use the assumption in our proof. Hopefully this makes sense:



Which is divisible by 3, since M is an integer.

Step 3: Since the expression is divisible by three, then the result is true for . However, since the result is true for n=1, this means that by induction, it is true for n=1+1=2, n=2+1=3, etc, for all

Hope that this helped!