Math Is Fun Forum

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

induction quick please :P

ive got exam tomorrow so hopefully ill get an answer before then ^^

prove by induction:

prove that

i worked it like this:

i always get confused with induction whether im doing it the right way or not. is this correct?

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Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: induction quick please :P

That's right, just make sure that you are explicit with the base case, inductive hypothesis, and conclusion.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: induction quick please :P

ok thanks. And yeh actually i forgot to explicitily show the base case for A[sub]0[/sub]

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The Beginning Of All Things To End.
The End Of All Things To Come.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: induction quick please :P

In higher level classes where you use induction rather than being tested on it, it's very typical to prove what you need to and then just say, "and proceed by induction."  No base case or hypothesis.  But most teachers/professors want to see everything very explicit when you are first learning it.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."