Chapter 5 数列与级数 - 公式表

\[a_n = a_1 + (n-1)d\]

\[S_n = \frac{n}{2}[2a_1 + (n-1)d]\] \[S_n = \frac{n}{2}(a_1 + a_n)\]

\[a_n = a_1 \cdot r^{n-1}\]

\[S_n = \frac{a_1(1-r^n)}{1-r} \text{ (当 } r \neq 1\text{)}\] \[S_n = na_1 \text{ (当 } r = 1\text{)}\]

\[S_{\infty} = \frac{a_1}{1-r} \text{ (当 } |r| < 1\text{)}\]

\[|r| < 1 \text{ 时级数收敛}\] \[|r| \geq 1 \text{ 时级数发散}\]

\[\sum_{i=1}^{n} (a_i + b_i) = \sum_{i=1}^{n} a_i + \sum_{i=1}^{n} b_i\] \[\sum_{i=1}^{n} ka_i = k\sum_{i=1}^{n} a_i\]

\[\sum_{i=1}^{n} i = \frac{n(n+1)}{2}\] \[\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6}\]

\[a_{n+1} = f(a_n)\]

\[a_{n+1} = ra_n + d\]