查看“︁数学/求和表”︁的源代码

==有限和==


*<math>q\neq 1</math>时，若<math>a_{i}=a_{0}q^{i}</math>，则
<math>
  \sum_{i=0}^{n}a_{i}=a_{0}\frac{1-q^{n+1}}{1-q}.
</math>


==无限和==
===等比级数===
*<math>|q|<1</math>时，若<math>a_{i}=a_{0} q^{i}</math>，则
<math>
  \sum_{i=0}^{\infty}a_{i}=\frac{a_{0}}{1-q}.
</math>
===<math>\zeta</math>函数===
*<math>\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}</math>
*<math>\sum_{n=1}^{\infty}\frac{1}{n^4}=\frac{\pi^4}{90}</math>