### Finding the finite formula for the infinite sum

1) When is sin(x)=0? Why is it plausible that sin(x)=x(1-x/pi)(1+x/pi)(1-x/2*pi)(1+x/2*pi) ... ? 2) Explain how Euler concludes from 1) that pi^2/6=1+1/4+1/9+1/16 ... . 3) Compare the formula in 2) to Archimedes' calculation for pi. Which of these methods is more efficient and why? 4) Why does the argument from 3) not w