Have a look at this Page
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
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?
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.