A) \[(-\infty ,-10]\]
B) \[(10,\infty )\]
C) \[(0,10)\]
D) \[(-10,0)\]
Correct Answer: C
Solution :
first term \[=b\] common ration\[=d\] \[-1<d<1\] for infinite series For infinite series ; \[S=\frac{b}{1-d}=5\] \[\to b=5(1-b)\] interval of\[b=(0,10)\] Let \[r\] be the common ration of the series, then the sum of the series is \[\frac{b}{1-r}=5\]. Clearly, \[b=5(1-r)\]. Since \[|r|<1\] for an infinite geometric series to converge, we have \[-1<r<1\Rightarrow 0<1-r<2\Rightarrow 0<b<10\]. So option C is the correct answer.
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