Chapter 7: Q.1 (page 652)
true /false : determine whether ah of the statement that follow is true or false .if a statement is true , explain why. if a statement is false ,provide a counter example .
a) true or false : is an alternating series
b) true or false : if an the alternating series converges, then the series converges
c) true or false : if an the series converges, then the series also converges absolutely .
d) true or false : if a function f satisfies the hypothesis of the integral test, then the series converges
e) true or false : if a series converges conditionally , then the series diverges.
f) true or false : if is a series such that , then the series converges conditionally.
g) true or false : if is a series such that , then the series converges absolutely
h) true or false : if we rearrange infinitely many terms of the alternating harmonic series , we can change the value of its sum
Short Answer
a)false
b)true
c)true
d)false
e)true
f)false
g)true
h)true