MATH 128A, SUMMER 2010, HOMEWORK 2 SOLUTIONBENJAMIN JOHNSONHomework 2: Due Wednesday, June 301.3; 1ab, 6b, 13b, 162.1; 2b, 13, 172.2; 1d, 4, 8, 17section 1.31.a. Use three-digit chopping arithmetic to compute the sum∑10i=1(1/i2) first by11+4+· · ·+1100and then by1111. Which method is more accurate and why?1
b. Write an algorithm to sum the finite series∑Ni=1xiin reverse order.
6. Find the rate of convergence of the following sequences asn→ ∞.b. limn→∞sin1n2
13.b. Make a table listing 1/n, 1/n2, 1/n3, and 1/n4forn= 5, 10, 100, and 1000, and discussthe varying rates of convergence of these sequences asnbecomes large.
Date: June 30, 2010.1