# Thread: sequence limit and convergence

1. ## sequence limit and convergence

have been given sequence

bn = 2n-9/(10(0.5)^n)+2

i trying to find if it converges or not and the limit.
any ideas would be welcomed.

2. Hi

Could you rewrite with parentheses so that we can understand which are the numerator and the denominator ?

3. 2n-9 numerator
10(0.5)^n +2 denominator

we have 10(0.5)^n plus 2 and not n+2 as power

hope this helps

4. OK so $b_n = \frac{2n-9}{10(0.5)^n+2}$

What is the limit of the numerator ? What is the limit of the denominator ?

5. for denominator as n gets larger (0.5)^n will converge to 0 so limit will be 2
but 2n-9 will increase as n gets larger not sure what happen guess it will not be convergent.

i am guessing the sequence will behave like-9/2 mulitiply by 2n which is not convergent ?