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Question

limx1x+x2+...+xnnx1 equals

A
n
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B
0
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C
n22
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D
n(n+1)2
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Solution

The correct option is D n(n+1)2
Using L-hospital's rule,
limx1x+x2+...+xnnx1
=limx11+2x+3x2+...+nxn11
=1+2+3+.....................+n=n2(2+(n1).1)
=n(n+1)2
Hence, option 'D' is correct.

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