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An infinite G.P. has first term ' \(x\) ' and sum ' 5 ', then \(\mathrm{x}\) belongs to
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Verified Answer
The correct answer is:
\(0 < x < 10\)
\(\frac{\mathrm{x}}{1-\mathrm{r}}=5 \Rightarrow \mathrm{r}=1-\frac{\mathrm{x}}{5}\)
Since, G.P. contains infinite terms
\(\begin{aligned}
& \therefore-1 < \mathrm{r} < 1 \\
& \Rightarrow-1 < 1-\frac{\mathrm{x}}{5} < 1 \Rightarrow 0 < \mathrm{x} < 10, \mathrm{x} \neq 5
\end{aligned}\)
Since, G.P. contains infinite terms
\(\begin{aligned}
& \therefore-1 < \mathrm{r} < 1 \\
& \Rightarrow-1 < 1-\frac{\mathrm{x}}{5} < 1 \Rightarrow 0 < \mathrm{x} < 10, \mathrm{x} \neq 5
\end{aligned}\)
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