Editing Square pyramidal number (section)

==Other properties==
The [[alternating series]] of [[unit fraction]]s with the square pyramidal numbers as denominators is closely related to the [[Leibniz formula for π|Leibniz formula for {{pi}}]], although it converges faster. It is:{{r|fearnehough}}
<math display=block>
\begin{align}
\sum_{i=1}^{\infty}& (-1)^{i-1}\frac{1}{P_i}\\
&=1-\frac{1}{5}+\frac{1}{14}-\frac{1}{30}+\frac{1}{55}-\frac{1}{91}+\frac{1}{140}-\frac{1}{204}+\cdots\\
&=6(\pi-3)\\
&\approx 0.849556.\\
\end{align}
</math>

In [[approximation theory]], the sequences of odd numbers, sums of odd numbers (square numbers), sums of square numbers (square pyramidal numbers), etc., form the coefficients in a method for converting [[Chebyshev approximation]]s into [[polynomial]]s.{{r|menza}}