北京邮电大学 计算机学院 离散数学 2.4-Sequences and Summations-2014.ppt

* College of Computer Science Technology, BUPT -- ? Copyright Yang Juan Nested Summations These have the meaning you’d expect. Note issues of free vs. bound variables, just like in quantified expressions, integrals, etc. * College of Computer Science Technology, BUPT -- ? Copyright Yang Juan Some Shortcut Expressions Geometric series. Euler’s trick. Quadratic series. Cubic series. * College of Computer Science Technology, BUPT -- ? Copyright Yang Juan Using the Shortcuts Example: Evaluate . Use series splitting. Solve for desiredsummation. Apply quadraticseries rule. Evaluate. * College of Computer Science Technology, BUPT -- ? Copyright Yang Juan Summations: Conclusion You need to know: How to read, write evaluate summation expressions like: Summation manipulation laws we covered. Shortcut closed-form formulas,  how to use them. * College of Computer Science Technology, BUPT -- ? Copyright Yang Juan Homework §2.4 6(a,c,e,g), 12(a,d), 18, 26(a,f), 30(b,d), 34(b) College of Computer Science Technology, BUPT -- ? Copyright Yang Juan Yang Juan yangjuan@bupt.edu.cn College of Computer Science Technology Beijing University of Posts Telecommunications Sequences and Summations * College of Computer Science Technology, BUPT -- ? Copyright Yang Juan Sequences Definition: A sequence is a function from a subset of the natural numbers (usually of the form {0, 1, 2, . . . } to a set S. Note: the sets {0, 1, 2, 3, . . . , k} and {1, 2, 3, 4, . . . , k} are called initial segments of N. Notation: if f is a function from {0, 1, 2, . . .} to S we usually denote f(i) by ai and we write {a0, a1, a2, a3, . . . } = = where k is the upper limit (usually ?). * College of Computer Science Technology, BUPT -- ? Copyright Yang Juan Sequence Examples Some authors write “the sequence a1, a2, …” instead of {an}, to ensure that the set of indices is clear. Be careful: Our book often leaves the indices ambiguous. An example