Question

Consider the sequence 2/4, 3/5, 4/6, 5/7,... Which statement describes the sequence?

Answer 1

Answer:

The sequence converges to 1.

Step-by-step explanation:

Sequence 2/4, 3/5, 4/6, 5/7

This sequence can be summarized as:

$\sum_{n=0}^{\infty} \frac{n+2}{n+4}$

To test if it converges, we can calculate the limite of $\frac{n+2}{n+4}$ as n goes to infinite.

Limit:

$\lim_{n \rightarrow \infty} \frac{n+2}{n+4}$

Considering only the terms with the highest exponent in the numerator and the denominator:

$\lim_{n \rightarrow \infty} \frac{n+2}{n+4} = \lim_{n \rightarrow \infty} \frac{n}{n} = \lim_{n \rightarrow \infty} 1 = 1$

Thus, the sequences converges to 1.