(a) Using computer or tables (or see Chapter 7, Section 11), verify that P[infinity] n=1 1/n2 = π2/6=1.6449+, and also verify th
at the error in approximating the sum of the series by the first five terms is approximately 0.1813. (b) By computer or tables verify that P[infinity] n=1(1/n2)(1/2)n = π2/12−(1/2)(ln 2)2 = 0.5822+, and that the sum of the first five terms is 0.5815+. (c) Prove theorem (14.4). Hint: The error is | P[infinity] N+1 anxn|. Use the fact that the absolute value of a sum is less than or equal to the sum of the absolute values. Then use the fact that |an+1|≤|an| to replace all an by aN+1, and write the appropriate inequality. Sum the geometric series to get the result.
