Thread: Simple induction help

Hi,

I have a very simple induction problem that i'd like help solving.

Prove that for all positive Integers n, that :


I know that the first step is to replace n with n+1 but then what?

/Jones

Hello,

Originally Posted by Jones

Hi,

I have a very simple induction problem that i'd like help solving.

Prove that for all positive Integers n, that :


I know that the first step is to replace n with n+1 but then what?

/Jones

The first step is to prove it is true for n=1.
The second step is to state the inductive hypothesis, that is to say assuming that

The third step is to prove that it is true if you "replace" n by n+1, that is to say :


Now, use the inductive hypothesis to substitute

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Another way would have been to note that and use telescoping series (Telescoping series - Wikipedia, the free encyclopedia)

Hmm, how do you mean?

isn't it just a simple matter of:

I'd do it like this:

Proving it true for n=1:






True for n=1.

That's the easy bit. I'll leave it up to you to do the rest.