分部求和法

分部求和法（英语：Summation by parts）也叫阿贝尔变换（英语：Abel transformation，有别于Abel transform）或阿贝尔引理（英语：Abel's lemma）是求和的一种方法。设 $\{f_k\}$ 和 $\{g_k\}$ 为两个数列，则有

\sum_{k=m}^n f_k(g_{k+1g_k) = \left[f_{n}g_{n+1} - f_m g_m\right] - \sum_{k=m}^n g_{k+1}(f_{k+1 f_k)

.

它被用来证明积分第二中值定理。

分部求和公式也可被写成比较对称的方式：

\sum _{i=m+1}^n \left(b_i-b_{i-1}\right) a_i+\sum _{i=m+1}^n \left(a_i-a_{i-1}\right) b_{i-1} =a_n b_n-a_m b_m =\sum _{i=m+1}^n \left(b_i-b_{i-1}\right) a_{i-1}+\sum _{i=m+1}^n \left(a_i-a_{i-1}\right) b_i

单词	Summation by parts
释义	Summation by parts 中文百科分部求和法分部求和法（英语：Summation by parts）也叫阿贝尔变换（英语：Abel transformation，有别于Abel transform）或阿贝尔引理（英语：Abel's lemma）是求和的一种方法。设 $\{f_k\}$ 和 $\{g_k\}$ 为两个数列，则有 $\sum_{k=m}^n f_k(g_{k+1g_k) = \left[f_{n}g_{n+1} - f_m g_m\right] - \sum_{k=m}^n g_{k+1}(f_{k+1 f_k)$ . 它被用来证明积分第二中值定理。分部求和公式也可被写成比较对称的方式： $\sum _{i=m+1}^n \left(b_i-b_{i-1}\right) a_i+\sum _{i=m+1}^n \left(a_i-a_{i-1}\right) b_{i-1} =a_n b_n-a_m b_m =\sum _{i=m+1}^n \left(b_i-b_{i-1}\right) a_{i-1}+\sum _{i=m+1}^n \left(a_i-a_{i-1}\right) b_i$ 英语百科 Summation by parts 分部求和法 In mathematics, summation by parts transforms the summation of products of sequences into other summations, often simplifying the computation or (especially) estimation of certain types of sums. The summation by parts formula is sometimes called Abel's lemma or Abel transformation.
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Summation by parts

分部求和法

Summation by parts 分部求和法