Determine whether the geometric series is convergent or divergent. 8 + 7 + 49/8 + 343/64 + …

Solution:

In the geometric series 8 + 7 + 49/8 + 343/64 + …

a = first term = 8

So the ratio r of a term and its preceding term is = 7/8 = (49/8)/7 = (343/64)/(49/8) = 7/8 = 0.875

It is a geometric series.

In this case, |r| < 1 the series is convergent and the sum of an infinite geometric series is written as a/(1 - r)

Substituting the values

= 8/(1 - 0.875)

By further calculation

= 8/0.125

= 64

Therefore, the geometric series is convergent.

Determine whether the geometric series is convergent or divergent. 8 + 7 + 49/8 + 343/64 + …

Summary:

The given geometric series 8 + 7 + 49/8 + 343/64 + … is convergent.