# Sequence and Series Problems

• May 7th 2013, 03:50 AM
Lawati9
Sequence and Series Problems
Hello everyone

I'm having trouble with these three questions and would like some help

the questions are :

(a) Can you give an example of a sequence which is increasing,

(b) Can you give an example of a convergent sequence {an} such that

(c) Can you give an example of a divergent sequence {an} such that

for the first question i thought of (-1)^n but its bounded from above and below and can't prove that it is increasing

for second question i think 1/n is the answer , as the sequence converges to 0 but the series diverges because it's a harmonic series

for the third question i have no idea at all

• May 7th 2013, 04:02 AM
Prove It
Re: Sequence and Series Problems
b) The harmonic series is divergent while its terms converge to 0.

c) No, in order for a series to be convergent, the terms HAVE to converge to 0.
• May 7th 2013, 04:06 AM
Plato
Re: Sequence and Series Problems
Quote:

Originally Posted by Lawati9
the questions are :
(a) Can you give an example of a sequence which is increasing,

(b) Can you give an example of a convergent sequence {an} such that

(c) Can you give an example of a divergent sequence {an} such that
c) There is a theorem: $\sum\limits_{n = 1}^\infty {{a_n}}$ converges only if $(a_n)\to 0~.$