G 6. Provide an example of (a) a geometric series that diverges. (b) a geometric series PN n=0 an, that starts at n = 0 and converges. Find its sum. (c) a geometric series PN n=1 an, that starts at n = 1 and converges. Find its sum. (d) Explain how the sums for a geometric series that starts at n = 0 differs from the same series that starts at n = 1.

Check step-by-step-explanation.

Step-by-step explanation:

A given criteria for geometric series of the form is that . Other wise, the series diverges. When it converges, we know that

.

So,

a) diverges since

b)converges since , and

c)We can use the series in b) but starting at n=1 instead of n=0. Since they differ only on one term, we know it also converges and

.

d)Based on point c, we can easily generalize that if we consider the following difference

So, they differ only by 1 if the series converges.

final answer is : )

109 is the nearest whole number/final answer! : )