WIKI
(1+x+x2+x3+…)=11−x(1+x2+x4+x6+…)=11−x2
(1+x+x2+x3+x4)=1−x51−x
数论a为等比数列,首项a1公比qn∑i=1ai=a1(1−qn)1−q
\begin{align} (a+b)^n&=\sum\limits^n_{k=0}\binom{n}{k}a^kb^{n-k}\\ \binom{n}{k}&=\frac {P^k_n} {k!}=\frac{k!}{k!(n-k)!}\\ (1+x)^n&=\sum\limits^\infty_{k=0}\binom{n}{k}x^k\\ \frac 1 {(1-x)^n}&=\sum\limits^\infty_{k=0}\binom{n+k-1}{k}x^k\\\ e^x&=\sum\limits_{i=0}^\infty\frac 1{i!}x^i \end{align}