Infinite Product -- from Wolfram MathWorld
and your third can be written in closed form
Hi, I've been asked to find the value of some infinite products. We've done infinite series before, but not products. There's a few questions - if someone could help me out with the first one, I could try the other two myself.
Question: Find the values of the following infinite products:
For example, . Therefore
For you can do the same thing. Factorise as , write down the product of the first few terms and see how they telescope. You should then be able to show that the product of the first N terms converges to 2/3 as N→∞.