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Question

If 1+2x+3x2+4x3++4, (|x|<1), then

A
least value of x is 12
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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++(1x)S=1+x+x2+x3++(1x)S=11xS=1(1x)24(x1)21412(x1)1212x32
Also,
|x|<1
So,
12x<1

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