MATH 2B Chapter Notes - Chapter 11.3: Integral Test For Convergence, Ibm System P

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2B
• Professor: George Donaldson

Document Summary

11. 3 the integral test and estimates of sums. Much of the discussion of series involves methods or tests which may be applied to see if a series converges or diverges. Each test applies to different types of series and has different advantages and disadvantages. The integral test is our second of these (after the nth-term test). It formalizes the intuitive idea that integrals, being de ned using limits of sums, should behave similarly to in nite series. The graph of a decreasing, positive function f is drawn, where f has domain [1, ). The sequence (an) n=1 is de ned by an = f (n). x f a1 a2 a3 a4a5. 6 n 1 n n + 1 x. Notice that each of the rectangles has base 1 and height equal to one of the values ai of the sequence. The areas of the rectangles are therefore equal to values of the sequence.