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Question

If |x|<1, then limx(1+x)(1+x2)(1+x4)+...(1+x2n)=

A
11+x
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B
11x
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C
1
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D
0
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Solution

The correct option is D 0
limx(1+x)(1+x2)(1+x4).....(1+x2x)
limx(1x)(1+x)(1+x2)(1+x4)....(1+x2x)(1x)
=limx(1x2)(1+x2)(1+x4).....(1+x)2x(1x)
=limx1x4x1x As |x|<1
=limx101x=0

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