Monotonic 0<an<1 for all n and no two terms are the same

1. Dec 20, 2011

gregy6196

1. The problem statement, all variables and given/known data

Give an example of a sequence {an}, satisfying the following:
{an} is monotonic
0<an<1 for all n and no two terms are the same
lim(n→∞) an = 1/2

2. Relevant equations
what is monotonic

3. The attempt at a solution
1/(2√n)
n/(2n-1)
1/2^n

just been trying genearal sequences but none of them work

2. Dec 20, 2011

dirk_mec1

Re: sequence

Does this one work?

$$a_n = \frac{1}{2 } + \frac{1}{n}\ \forall n>2$$

3. Dec 20, 2011

gregy6196

Re: sequence

what would be the first term?

4. Dec 20, 2011

HallsofIvy

Staff Emeritus
Re: sequence

Oh, c'mon! Use any two numbers less than 1/2 for a1 and a2.

5. Dec 20, 2011

bennyska

Re: sequence

monotonic refers to how it increases. monotonic increasing means each term is greater than or equal to the term before it. monotonic decreasing means each term is less than or equal to the term before it. if it just says monotonic, either situation will work.

6. Dec 24, 2011

Re: sequence

For all n