Statement-1 : The largest interval for which we can find the sum of the series 1+(2x−1)+(2x−1)2+(2x−1)3+…) is (0,1)Statement-2 : An infinite geometric series a+ar+ar2+… can be summed up if |r|<1

|2x−1|<1⇒−1<2x−1<1⇒ 0<x<1

Statement-1 : The largest interval for which we can find the sum of the series 1+(2x−1)+(2x−1)2+(2x−1)3+…) is (0,1)Statement-2 : An infinite geometric series a+ar+ar2+… can be summed up if |r|<1

|2x−1|<1⇒−1<2x−1<1⇒ 0<x<1

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Statement-1 : The largest interval for which we can find the sum of the series $1 + (2 x - 1) + (2 x - 1)^{2} + (2 x - 1)^{3} + \dots)$ is $(0, 1)$
Statement-2 : An infinite geometric series $a + a r + a r^{2} + \dots$ can be summed up if $| r | < 1$

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STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for

STATEMENT-1

STATEMENT-1 is True, STATEMENT-2 is False

STATEMENT-1 is False, STATEMENT-2 is True

answer is A.

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$\begin{array}{l} | 2 x - 1 | < 1 \Rightarrow - 1 < 2 x - 1 < 1 \\ \Rightarrow 0 < x < 1 \end{array}$

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Statement-1 : The largest interval for which we can find the sum of the series 1+(2x−1)+(2x−1)2+(2x−1)3+…) is (0,1)Statement-2 : An infinite geometric series a+ar+ar2+… can be summed up if |r|<1

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Statement-1 : The largest interval for which we can find the sum of the series $1 + (2 x - 1) + (2 x - 1)^{2} + (2 x - 1)^{3} + \dots)$ is $(0, 1)$
Statement-2 : An infinite geometric series $a + a r + a r^{2} + \dots$ can be summed up if $| r | < 1$