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B
greatest value of x is 43
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C
least value of x is 23
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D
greatest value of x deos not exist
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Solution
The correct options are A least value of x is 12 D greatest value of x deos not exist Let, S=1+2x+3x2+4x3+⋯+∞xS=1x+2x2+3x3+⋯+∞⇒(1−x)S=1+x+x2+x3+⋯+∞⇒(1−x)S=11−x⇒S=1(1−x)2≥4⇒(x−1)2≤14⇒−12≤(x−1)≤12⇒12≤x≤32 Also, |x|<1 So, 12≤x<1