Question

PLEASE HELP HOMEWORK

Answer 1

Answer:

Option (1)

Step-by-step explanation:

As we know, sum of an infinite geometric series,

$S=\frac{a}{1-r}$

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 = $\frac{301.3}{4.2}$ = 1.15

Since |r| = 1.15 > 1

Series will diverge

Option (2),

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

Common ratio = $\frac{3.57}{4.2}$ = 0.85

Since |r| < 1

Series will converge.

Option (3),

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

Common ratio = $\frac{729}{6651}$ = 0.11

Since |r| < 1

Series will converge.

Option (4),

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

Common ratio = $\frac{50}{100}=\frac{1}{2}$

Since |r| < 1

Series will converge.

Option (1) will be the answer.