Find the sum of the series $0.9 + 0.09 + 0.009 + 0.0009 + \cdots$ .
A)9
B)0
C)0.999
D)0.9999
E)9.9
F)2
G)1
H)Divergent

Name: Find the sum of the series $0.9 + 0.09 + 0.009 + 0.0009 + \cdots$ . A)9 B)0 C)0.999 D)0.9999 E)9.9 F)2 G)1 H)Divergent
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Quizplus · Accepted Answer

The series is a geometric series with the first term $a = 0.9$ and common ratio $r = 0.1$. The sum of an infinite geometric series is given by $S = \frac{a}{1-r}$, which in this case is $\frac{0.9}{1-0.1} = 1$.

Find the Sum of the Series 0.9+0.09+0.009+0.0009+⋯0.9 + 0.09 + 0.009 + 0.0009 + \cdots0.9+0.09+0.009+0.0009+⋯

Find the Sum of the Series $0.9 + 0.09 + 0.009 + 0.0009 + \cdots$