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

[gregy6196]

Homework Statement

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

Homework Equations

what is monotonic

The Attempt at a Solution

1/(2√n)
n/(2n-1)
1/2^n

just been trying genearal sequences but none of them work

 

[dirk_mec1]

Does this one work?

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

 

[gregy6196]

what would be the first term?

 

[HallsofIvy]

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

 

[bennyska]

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.

 

[gregy6196]

Does this one work?

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

For all n