Thread: induction

I have the cartesian product of this:

1 - (1/(k^2)) from k = 2 to n.

I picked random values of n like n = 2, 3, 4.

With n = 2, I have (1 - (1/4)).
With n = 3, I have (1 - (1/4)) * (1 - (1/9)).
With n = 4, I have (1 - (1/4)) * (1 - (1/9)) * (1 - (1/16)).
etc.

How do I go about finding a formula for this for all n?

I know that 1 - (1/(k^2)) = ((k + 1)(k - 1))/k^2.

Thanks in advance for any help.

Hello, PvtBillPilgrim!

I have the cartesian product of this: .

How do I go about finding a formula for this?

You should have examined those cases more closely . . .





It appears that the general form is: .

The next task is to prove it . . .