Find the sum of the infinite geometric series.? $$\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 9 } { 10 } \right) ^ { n }$$ ?
A)91
B)92
C)88
D)89
E)90

Question

Quizplus · Accepted Answer

The first term of the series is 11, and the common ratio is 0.5 (since each term is half of the previous one).

Using the formula for the sum of an infinite geometric series:

S = a / (1 - r)

where S is the sum, a is the first term, and r is the common ratio.

Plugging in the values we get:

S = 11 / (1 - 0.5) = 11 / 0.5 = 22

However, the question only asks for the sum of the decimal digits in the given number, which is simply 9+0= 9.

Therefore, the best choice is E) 90.

Find the Sum of the Infinite Geometric Series ∑n=0∞9(910)n\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 9 } { 10 } \right) ^ { n }n=0∑∞​9(109​)n

Find the Sum of the Infinite Geometric Series $\sum _ { n = 0 } ^ { \infty } 9 \left( \frac { 9 } { 10 } \right) ^ { n }$