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9-99.

Consider the infinite series below. For each, decide if it converges or diverges and justify your conclusion. If the series converges, find its sum.

Hint:

For an infinite geometric series:

$4 + 4 + 4 + 4 + ...$
Hint (a):
This is a geometric series with $r = 1$ .

$\frac { 1 } { 10 } + \frac { 1 } { 100 } + \frac { 1 } { 1000 } + \ldots$
Hint (b):
This is a geometric series with $r = 1/10$ .

$10 + 9 + 8 + 7 + ...$
Hint (c):
This is an arithmetic series. Does an infinite arithmetic series have a finite sum?

$- 2 + \frac { 6 } { 5 } - \frac { 18 } { 25 } + \frac { 54 } { 125 } - \dots$
Hint (d):
This is a geometric series with $r =-3/5$ .

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