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Question

The value oflimx1xn+xn1+xn2+.......+x2+xnx1


A

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B

0

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C

1

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D

n

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Solution

The correct option is A


limx1xn+xn1+xn2+.......+x2+xnx1(00form)=limx1{(xn1)(x1)+(xn11)(x1)+.......+(x1)(x1)}
Using L'Hospital Rule we get -
=n+(n1)+.......+2+1=n(n+1)2


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