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Question

12x2+23x3+34x4+45x5+=

A
x1x+log(1x)
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B
x1+x+log(1x)
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C
x1x+log(1+x)
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D
x1+x+log(1+x)
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Solution

The correct option is A x1x+log(1x)
Let y=12x2+23x3+34x4+45x5+
y=(112)x2+(113)x3+(114)x4+(115)x5+
y=(x2+x3+x4+)(12x2+13x3+14x4+15x5+)
y=x21x(log(1x)x)=x1x+log(1x)
Note: Here assumption is that |x|<1

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