MAT137Y1 Lecture Notes - Lecture 26: Arithmetic Progression, Geometric Progression, Royal Institute Of Technology
MAT137Y1 verified notes
26/39View all
Document Summary
Sequences converging to zero: we say that the sequence sn converges to 0 whenever the following hold: for all (cid:0) > 0, there exists a real number, n, such that n > n = . |sn: a sequence of real numbers {ak} is a function from the positive integers to the real numbers. For each positive integer index k, the output ak is called the kth term of the sequence. A sequence {ak} is said to be recursively defined if there is some index k so that for k > k, the value of ak is determined by a1,a2,,ak 1. The equation defining ak in terms of a 1, a 2, . A geometric sequence is a sequence in which each term differs from the previous term by a constant multiplicative factor r. we will commonly desire to start such sequences at k = 0:
