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8-123.

Find the sum of the following infinite geometric series. If the answer is “ $∞$ ,” explain why.

Hint:

$S=\frac{a}{1-r}$

$1 +\frac { 1 } { 2 }+\frac { 1 } { 4 }+\frac { 1 } { 8 }\:+\:...$

$16 + 4 + 1 +\frac { 1 } { 4 }+\frac { 1 } { 16 }\:+\: ...$

$a + 0.9a + 0.81a + 0.729a + …$
Hint (c):
$r = 0.9$

$1 + 1.1 + 1.21 + 1.331 + …$
Hint (d):
What happens when $r > 1$ ?

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