Failed to parse (syntax error): {\displaystyle \sum_{n=s}^t C\cdot f(n) = C\cdot \sum_{n=s}^t f(n)\text{, onde C é uma constante. }
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{\displaystyle \sum _{n=s}^{t}f(n)+\sum _{n=s}^{t}g(n)=\sum _{n=s}^{t}\left[f(n)+g(n)\right]}
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{\displaystyle \sum _{n=s}^{t}f(n)-\sum _{n=s}^{t}g(n)=\sum _{n=s}^{t}\left[f(n)-g(n)\right]}
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{\displaystyle \sum _{i=m}^{n}f(i)=\sum _{i=m+p}^{n+p}f(i-p)}
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{\displaystyle \sum \limits _{n=s}^{t}j=\sum \limits _{n=1}^{t}j-\sum \limits _{n=1}^{s-1}j}
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{\displaystyle \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}
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{\displaystyle \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.}}}
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{\displaystyle \sum _{i=0}^{n}i=\sum _{i=1}^{n}i={\frac {n(n+1)}{2}}}
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{\displaystyle \sum \limits _{k=0}^{n-1}{2^{k}}=2^{n}-1}
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{\displaystyle \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}}
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{\displaystyle \sum _{i=0}^{n}i^{3}=\left(\sum _{i=0}^{n}i\right)^{2}}
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{\displaystyle \sum _{i=m}^{n-1}a^{i}={\frac {a^{m}-a^{n}}{1-a}}(m<n)}
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{\displaystyle \sum _{i=0}^{n-1}a^{i}={\frac {1-a^{n}}{1-a}}}
![{\displaystyle \sum _{n=s}^{t}f(n)+\sum _{n=s}^{t}g(n)=\sum _{n=s}^{t}\left[f(n)+g(n)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a762d789e2af544d36eeeefc783b61559d64dc84)
![{\displaystyle \sum _{n=s}^{t}f(n)-\sum _{n=s}^{t}g(n)=\sum _{n=s}^{t}\left[f(n)-g(n)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f3b63ace30b999de1bbdcf04f85ed8c7ce0b7a9a)
