PI 2 = 1 + 1 3 + 1 3 2 5 + 1 3 2 5 3 7

This equation is correct and represents Euler's formula for calculating pi/2. It is derived from the infinite product expansion of the sine function:

sin(x) = x * (1 - x^2 / pi^2) * (1 - x^2 / (4 pi^2)) * (1 - x^2 / (9 pi^2)) * ...

Setting x = pi/2 and simplifying the product gives:

pi/2 = 1 + 1/3 + 2/15 + 17/315 + 62/2835 + ...

The terms in this series are known as the Gregory-Leibniz series and converge to pi/4. Multiplying by 2 gives the desired result of pi/2.