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- August 16th 2010, 06:46 PMrozaWallis product.
- August 16th 2010, 07:53 PMVlasev
The first part is straightforward, just plug in x = 1. For the second part, what is meant by compare? Are you asked to show which one converges faster per the number of terms?

Btw, the Wallis product for pi is

[Math]\displaystyle \prod_{n=1}^{\infty} \frac{2n}{2n-1} \cdot \frac{2n}{2n+1} = \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \cdot \frac{6}{7} \cdot \frac{8}{7} \cdot \frac{8}{9} \cdots = \frac{\pi}{2}[/tex] - August 16th 2010, 09:24 PMchisigma
The Leibnitz series is...

(1)

... so that after 2n iterations the last summed term is ...

The Wallis product [in logarithmic version...] is...

(2)

... so that after 2n iterations the last summed term is ...

The two methods seem to be comparable in speed: both are very slow (Worried) ...

Kind regards