Somatório e Produtório

Propriedades de Somatório

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sum_{n=s}^t C\cdot f(n) = C\cdot \sum_{n=s}^t f(n)\text{, onde C é uma constante. }

$\sum _{n=s}^{t}f(n)+\sum _{n=s}^{t}g(n)=\sum _{n=s}^{t}\left[f(n)+g(n)\right]$

$\sum _{n=s}^{t}f(n)-\sum _{n=s}^{t}g(n)=\sum _{n=s}^{t}\left[f(n)-g(n)\right]$

$\sum _{i=m}^{n}f(i)=\sum _{i=m+p}^{n+p}f(i-p)$

$\sum \limits _{n=s}^{t}j=\sum \limits _{n=1}^{t}j-\sum \limits _{n=1}^{s-1}j$

$\sum _{n=s}^{j}f(n)+\sum _{n=j+1}^{t}f(n)=\sum _{n=s}^{t}f(n){\text{, note que }}s\leq j\leq t$

$\sum _{i=m}^{n}i={\frac {n(n+1)}{2}}-{\frac {m(m-1)}{2}}={\frac {(n+1-m)(n+m)}{2}},{\text{ progressão aritmética.}}$

$\sum _{i=0}^{n}i=\sum _{i=1}^{n}i={\frac {n(n+1)}{2}}$

$\sum \limits _{k=0}^{n-1}{2^{k}}=2^{n}-1$

$\sum _{i=s}^{m}\sum _{j=t}^{n}{a_{i}}{c_{j}}=\sum _{i=s}^{m}a_{i}\cdot \sum _{j=t}^{n}c_{j}$

$\sum _{i=0}^{n}i^{3}=\left(\sum _{i=0}^{n}i\right)^{2}$

$\sum _{i=m}^{n-1}a^{i}={\frac {a^{m}-a^{n}}{1-a}}(m<n)$

$\sum _{i=0}^{n-1}a^{i}={\frac {1-a^{n}}{1-a}}$