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
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?
To prove using induction that
Try to show that IF P(k) is true THEN P(k+1) will also be true.
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.