Question

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)

Answer 1

Answer:

$a_{i} = \frac{(-3)^{i}}{4\cdot i!}$ converges.

Step-by-step explanation:

The convergence analysis of this sequence is done by Ratio Test. That is to say:

$r = \frac{a_{n+1}}{a_{n}}$, where sequence converges if and only if $|r| < 1$.

Let be $a_{i} = \frac{(-3)^{i}}{4\cdot i!}$, the ratio for the expression is:

$r =-\frac{3}{n+1}$

$|r| = \frac{3}{n+1}$

Inasmuch $n$ becomes bigger, then $r \longrightarrow 0$. Hence, $a_{i} = \frac{(-3)^{i}}{4\cdot i!}$ converges.