Paradox Part 1

Let Pn be the proposition/statement.

We wish to find out if P1 is true.

Suppose P1 is true if P2 is true.
Suppose P2 is true if P3 is true.
Suppose Pn is true if Pn+1 is true.

Then P1 is true if P to infinity is true.

So does P to infinity exist? And if it exists, is the successive proposition after P to infinity true?

Paradoxical Popcorn.