Chapter 4.8, Problem 17E

Explain the key points and reasons for the establishment of 12.3.2(integral Test)

Use 12.4.2 to determine whether the infinite series on the right side of equation 12.6.5, 12.6.6 and 12.6.7 converges for every real number x.

use Cauchy Mean-Value Theorem to derive Corollary 12.6.2, and then derive 12.6.3

Explain the focus and reasons for establishment of 12.5.4

explain how to 12.3.1 from 11.3.6

use Corollary 12.6.2 and 12.6.3 to derive 12.6.4,12.6.5, 12.6.6 and 12.6.7

Explain the focus and reasons for establishment of 12.5.1(lim(n->infinite) and sigma of k=0 to n)

Explain the focus and reasons for establishment of 12.5.3 about alternating series. and explain the reason why (sigma k=1 to infinite)(-1)k+1/k = 1/1 - 1/2 + 1/3 - 1/4 + .... converges.

Explain the key points and reasons for the establishment of 12.3.2(integral Test)