Chapter 7: Q.1 (page 630)
Determine whether each of the statements that follow true or false . if a statement is true, explain why. if a statement is false , provide a counter example .
a) True or False : if for every x >0 and the improper integral converges, then the improper integral converges.
b) True or False : if for every x > 0 and then the improper integrals both converge.
c) True or False : if for every positive integer k, then the series converges .
d) True or False : if <b kfor every positive integer k, then the series diverges.
e) True or False : if for every positive integer k and the series converges, then the series converges.
f) True or False : if both diverge then diverges .
g) True or False : if are both positive for every positive integer k and =, then both converge.
h) True or False : if both converge, then is finite .
Short Answer
a) True
b) False
c) False
d) False
e) False
f) False
g) False
h) False