Question

determine whether the series is convergent or divergent. 1/2 3/4 1/8 3/16 1/32 3/64..... convergent or divergent correct?. if it is convergent, find its sum. (if the quantity diverges, enter diverges.)

Answer 1

Answer: The geometric series is convergent and the value is 16.

Explanation:

How to illustrate the information?

Recall that the sum of an infinite geometric series, S, given first term, t_1, and common ratio, r, is given by:

S = t_1/(1 - r)

Note that:

3 = (4)(3/4)

9/4 = (3)(3/4

27/16 = (9/4)(3/4)

So this a geometric series with t_1 = 4 and r = 3/4. Therefore:

4 + 3 + 9/4 + 27/16 + ... = 4/(1 - 3/4) = 4/(1/4) = 16

The correct option is 16.

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum 4+3+ 9/4 +27/16 +???

choices are

1. 3/4

2. 12

3. 4

4. divergent

5. 16