6月5日——定积分本质
Example1. \quad求极限
limn→∞∑i=1nsiniπnn+in.\mathop {\lim }\limits_{n \to \infty } \sum\limits_{i = 1}^n {\frac{{\sin \frac{{i\pi }}{n}}}{{n + \frac{i}{n}}}} .n→∞limi=1∑nn+nisinniπ.
SolveSolveSolve :
Example1. \quad求极限
limn→∞∑i=1nsiniπnn+in.\mathop {\lim }\limits_{n \to \infty } \sum\limits_{i = 1}^n {\frac{{\sin \frac{{i\pi }}{n}}}{{n + \frac{i}{n}}}} .n→∞limi=1∑nn+nisinniπ.
SolveSolveSolve :