MATH 1132Q Study Guide - Midterm Guide: Conditional Convergence, Monotonic Function, Improper Integral

• School: UConn
• Department: Mathematics
• Course: MATH 1132Q
• Professor: Thomas DeFranco

Document Summary

A sequence is a list of numbers written in definite order. A sequence is finite if there is a last number, and if there is no last number then the sequence is said to be infinite. A sequence is written as {(cid:1853)(cid:2869),(cid:1853)(cid:2870),(cid:1853)(cid:2871), (cid:1853), } or {(cid:1853)}=(cid:2869) . If the lim (cid:1853)=(cid:1838), where l is a real number, then the infinite sequence given by (cid:1853) converges, if the lim (cid:1853)= or does not exist, then the infinite sequence diverges. Suppose (cid:1853)= { +(cid:2869)}=(cid:2868) , is this sequence convergent or divergent? lim (cid:1853)= lim +(cid:2869)= lim +(cid:2869)= (cid:2869)(cid:2869)+(cid:2868)=(cid:883) Since the limit of the sequence is equal to 1, the sequence converges. The squeeze theorem states that if (cid:1853) (cid:3409)(cid:1854) (cid:3409)(cid:1855) for (cid:1866) (cid:3410)(cid:1866)(cid:2868) and lim (cid:1853)= lim (cid:1855)=(cid:1838), then the lim (cid:1854)=(cid:1838). Determine the limit of the sequence or state the limit does not exist. (cid:1854)= {cos } for n (cid:3410) (cid:883).