Finite formula for the infinite sum

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Reference no: EM13117953

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 work to show the formula in 1) is correct?

Reference no: EM13117953

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