Question

Consider the sequence Two-fourths, three-fifths, four-sixths, StartFraction 5 Over 7 EndFraction, ellipsis Which statement describes the sequence? The sequence diverges. The sequence converges to 0. The sequence converges to 1. The sequence converges to [infinity].

Answer 1

Answer:

The sequence converges to 1

Step-by-step explanation:

Given

$\frac{2}{4}. \frac{3}{5}, \frac{4}{6}, \frac{5}{7},...$

Require

Description of the sequence

The given sequence follows:

$\frac{2}{4}. \frac{3}{5}, \frac{4}{6}, \frac{5}{7},... \frac{n+1}{n+3}$

i.e.

$T_n = \frac{n+1}{n+3}$

For every term,

$\frac{n+1}{n+3} < 1$

In other words,

as the value of n increases, $\frac{n+1}{n+3}$ approaches 1

Hence, (c) is true