possible true or false questions EXAM 2

true or false

every bounded, monotonic sequence is convergent

true

every increasing sequence is bounded below

true

every decreasing sequence is bounded above

true

not all convergent sequences are bounded

false - all convergent sequences are bounded

not all bounded sequences are convergent

false

not all monotonic sequences are convergent

true

a series diverges if and only if the sequence diverges

true

(6/5)^n converges?

false - can be written as 6^n/5^n which does not equal zero which means this diverges

can we use the divergence test for (2/3)^n?

false - this limit equals 0 so we cannot use the divergence test

give an example of a sequence that is bounded by not monotonic

{(-1)^n}

give an example of a sequence that is convergent but not monotonic

{(-1)^n/n}

give an example of a series that is divergent and the limit is 0

1/n

The series (-1)^n x n^2 diverges by the Divergence Test.

true

is the series converges then the sequence converges to 0

true

if the series diverges then the sequence does not converge to 0

false

if the sequence does not converge then the series diverges

true

if the series converges then the absolute value of the series converges

false

if an > bn> 0 for all n and the series bn diverges then an diverges

true

if bn > an > 0 for all n and the series bn diverges then an converges

false

if the sequence an is increasing and the absolute value of an is < 10 then the sequence converges

true