Question

Use the limit rules to determine, whether the following sequences converge. Calculate the limit.
\(\Large b_{n}:= 2^{-n} + \frac{n(n+2)}{2(n+1)(n+3)}\)

Answer 1

one way:
expand/distribute and use l'hospital on the second term
the first term you should know the limit of

Answer 2

(you have to use l'hospital twice)

Answer 3

ok.. @TuringTest can you apply it ?

Answer 4

I have to go
I'll be back soon, but someone should be able to implement my recommendation, if not come up with a better solution

Answer 5

ok thanks...