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

The sequence converges to 1

Explanation:

Given

`(2)/(4). (3)/(5), (4)/(6), (5)/(7),...`

Require

Description of the sequence

The given sequence follows:

`(2)/(4). (3)/(5), (4)/(6), (5)/(7),... (n+1)/(n+3)`

i.e.

`T_n = (n+1)/(n+3)`

For every term,

`(n+1)/(n+3) < 1`

In other words,

as the value of n increases,
`(n+1)/(n+3)` approaches 1

Hence, (c) is true