Question

PLEASE HELP HOMEWORK

Answer 1

Option (1)

Explanation:

As we know, sum of an infinite geometric series,

`S=(a)/(1-r)`

Here a = first term of the series

and r = common ratio.

If |r| < 1 Series converges

If |r| ≥ 1 Series diverges

For Option (1),

S = 262 + 301.3 + 346.5.........

Common ratio =
`(301.3)/(4.2)` = 1.15

Since |r| = 1.15 > 1

Series will diverge

Option (2),

S = 4.2 + 3.57 + 3.0345..........

Common ratio =
`(3.57)/(4.2)` = 0.85

Since |r| < 1

Series will converge.

Option (3),

S = 6651 + 729 + 81........

Common ratio =
`(729)/(6651)` = 0.11

Since |r| < 1

Series will converge.

Option (4),

S = 100, 50, 25...........

Common ratio =
`(50)/(100)=(1)/(2)`

Since |r| < 1

Series will converge.

Option (1) will be the answer.