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Consider the following geometric series.
2 + 0.5 + 0.125 + 0.03125 + ........
1. Find the common ratio.
|r| = __________.
2. Determine whether the geometric series is convergent or divergent.
3. If it is convergent, find its sum. (If the quantity diverges, enter DIVERGES.)

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peterchristian1300

Answer:

1. |r| = 1/4. or 0.25

2. Since r < 1, the geometric series is convergent.

3. To obtain the sum, we consider the formula of obtaining the sum to infinity of a geometrical series;

S = a /(1 - r)

where a = 2 ( first term)

r = 0.25 ( common ratio)

Therefore:

S = 2 /( 1 - 0.25)

= 2 / 0.75

= 8/3 or 2.6667

Hence, the sum is 8/3

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