Which geometric series converges?

Option (1)

Step-by-step explanation:

In a geometric series,

Here r =

For |r| < 1, series will converge.

For |r| > 1, series will diverge.

Option (1)

Given geometric series is,

Common ratio =

                        =

Since,

Series will converge.

Option (2)

r =

Since, 2 > 1,

Series will diverge.

Option (3)

Common ratio 'r' =

Since, 3 > 1,

Series will diverge.

Option (4)

Common ratio 'r' =

Since, 6 > 1

Series will diverge.

Therefore, Option (1) will be the correct option.

180 square centimeters

step-by-step explanation:

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0