## Summation and Product

summation

$\sum_{i=1}^{n} a_n$

\sum_{i=1}^{n} a_n

\sum comes from sum. To write expressions below and above the sigma, use "_" and "^".

summation large

$\displaystyle \sum_{i=1}^n a_n$

\displaystyle \sum_{i=1}^n a_n

If you use displaystyle, the sigma will be larger. The formula will be placed above and below the sigma.

summation sample

$\begin{eqnarray} \sum_{ k = 1 }^{ n } k^2 = \overbrace{ 1^2 + 2^2 + \cdots + n^2 }^{ n } = \frac{ 1 }{ 6 } n ( n + 1 ) ( 2n + 1 ) \end{eqnarray}$

\begin{eqnarray}
\sum_{ k = 1 }^{ n } k^2
= \overbrace{ 1^2 + 2^2 + \cdots + n^2 }^{ n }
= \frac{ 1 }{ 6 } n ( n + 1 ) ( 2n + 1 )
\end{eqnarray}

Using overbrace, you can display a brace on the top of the formula, and if you set the superscript, you can write text on top of the brace.

product

$\prod_{ i = 0 }^n x_i$

\prod_{ i = 0 }^n x_i

\prod comes from product.

product large

$\displaystyle \prod_{i=0}^n x_i$

\displaystyle \prod_{i=0}^n x_i
product sample

$\begin{eqnarray} n! = \prod_{ k = 1 }^n k \end{eqnarray}$

\begin{eqnarray}
n! = \prod_{ k = 1 }^n k
\end{eqnarray}

This is a sample using factorial.

product sample 2

$\begin{eqnarray} \zeta (s) = \prod_{ p:\mathrm{ prime } } \frac{ 1 }{ 1-p^{-s} } \end{eqnarray}$

\begin{eqnarray}
\zeta (s)
= \prod_{ p:\mathrm{ prime } }
\frac{ 1 }{ 1-p^{-s} }
\end{eqnarray}

This is a sample using the Riemann zeta function.

Formula
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