Hi I need help in regards with proving this problem.

If the sequence is 1,13,37,73,121

then it should follow like this 1+12+24+36......12n+(12n+12)

For the formula 6n^2 - 6n + 1.

How would I go on to prove this with induction exactly? Thanks

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- May 26th 2011, 12:55 PMmonkbearInduction help
Hi I need help in regards with proving this problem.

If the sequence is 1,13,37,73,121

then it should follow like this 1+12+24+36......12n+(12n+12)

For the formula 6n^2 - 6n + 1.

How would I go on to prove this with induction exactly? Thanks - May 26th 2011, 01:08 PMPlato
Have a look at this Page

- May 26th 2011, 02:08 PMbryangoodrich
Induction works in two steps. First you prove it true for some base case. In this case, if P(n) reads

show that P(0) is true. That should be straight-forward computation. The inductive step is to assume it is true for some . Assuming P(k), demonstrate P(k+1). By establishing those two facts regarding P(n), you can prove it is true for every . Do you understand why this two-step process works? In other words, do you know why the principle of mathematical induction (PMI) is a valid rule of inference?

That link didn't work for me Plato (using FF2). Broken? - May 26th 2011, 02:18 PMPlato
- May 26th 2011, 03:14 PMbryangoodrich
I've never used Wolfram Alpha before, but I have to say ... that's awesome!

- May 27th 2011, 04:20 AMArchie Meade
You should have a closer look at the pattern.

To prove using induction that

**P(k)**

**P(k+1)**

Try to show that**IF**P(k) is true**THEN**P(k+1) will also be true.

**Proof**

If P(k) is true, then P(k+1) is

which compares to

It remains to test the base case for n = 1, which is clearly true.