If you're seeing this message, it means we're having trouble loading external resources on our website.

# 求和符号

## 求和表示法的要素

$\begin{array}{rl}& \phantom{=}\sum _{n=1}^{3}2n-1\\ \\ & =\underset{n=1}{\underset{⏟}{\left[2\left(1\right)-1\right]}}+\underset{n=2}{\underset{⏟}{\left[2\left(2\right)-1\right]}}+\underset{n=3}{\underset{⏟}{\left[2\left(3\right)-1\right]}}\\ \\ & =1+3+5\\ \\ & =9\end{array}$

$n$ 是求和表达式中的 项数。当我们计算一个求和算式时，我们要分别用不同的取值替换算式中的项。

$\sum _{n=1}^{4}{n}^{2}=?$

$\begin{array}{rl}& \phantom{=}\sum _{n=4}^{6}n-1\\ \\ & =\underset{n=4}{\underset{⏟}{\left(4-1\right)}}+\underset{n=5}{\underset{⏟}{\left(5-1\right)}}+\underset{n=6}{\underset{⏟}{\left(6-1\right)}}\\ \\ & =3+4+5\\ \\ & =12\end{array}$

$\begin{array}{rl}& \phantom{=}\sum _{i=0}^{2}3i-5\\ \\ & =\underset{i=0}{\underset{⏟}{\left[3\left(0\right)\phantom{\rule{-0.167em}{0ex}}-\phantom{\rule{-0.167em}{0ex}}5\right]}}+\underset{i=1}{\underset{⏟}{\left[3\left(1\right)\phantom{\rule{-0.167em}{0ex}}-\phantom{\rule{-0.167em}{0ex}}5\right]}}+\underset{i=2}{\underset{⏟}{\left[3\left(2\right)\phantom{\rule{-0.167em}{0ex}}-\phantom{\rule{-0.167em}{0ex}}5\right]}}\\ \\ & =-5+\left(-2\right)+1\\ \\ & =-6\end{array}$

$\sum _{k=3}^{5}k\left(k+1\right)=$

$\sum _{n=1}^{4}\frac{k}{n+1}$

$\begin{array}{rl}& \phantom{=}\sum _{n=1}^{3}\frac{k}{n+1}\\ \\ & =\frac{k}{\left(1\right)+1}+\frac{k}{\left(2\right)+1}+\frac{k}{\left(3\right)+1}\\ \\ & =\frac{k}{2}+\frac{k}{3}+\frac{k}{4}\end{array}$

$\sum _{m=1}^{4}8k-6m=\phantom{\rule{0.167em}{0ex}}?$