Infinite Product - Seems to telescope Evaluate
$$\left(1 + \frac{2}{3+1}\right)\left(1 + \frac{2}{3^2 + 1}\right)\left(1 + \frac{2}{3^3 + 1}\right)\cdots$$
It looks like this product telescopes: the denominators cancel out (except the last one) and the numerators all become 3. 
What would my answer be?

we have the following identity (which affirms that the product telescopes):
$$\left (1+\frac{2}{3^n+1}\right)=3\cdot\frac{3^{n-1}+1}{3^n+1}=\frac{1+3^{-(n-1)}}{1+3^{-n}}$$
(as denoted in the comment by Thomas Andrews)and as a result:
$$\prod_{k=1}^n \left (1+\frac{2}{3^k+1}\right)=\frac{2\cdot 3^n}{3^n+1}=\frac{2}{1+3^{-n}}$$
