Question

Find the limit of the sequence described by the general expression 5n+ (-1) n /n^2
, or state that the limit does not exist.
a.1
b.0
c. 3
d. limit does not exist

Please select the best answer from the choices provided

Answer 1

Answer:

b. 0

Step-by-step explanation:

The expression can be rewritten as:

$A_{n} = \frac{5\cdot n}{n^{2}} + \frac{(-1)^{n}}{n^{2}}$

As n becomes greater and begins diverging to infinity, each component of the sum converges to zero. Then, the limit of the sequence is zero.