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Question

limnn2(x1/nx1/n+1),x>0, is equal to

A
0
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B
ex
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C
logex
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D
None of these
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Solution

The correct option is C logex
limnn2x1nx1n+1=limnn2.x1n+1x1n1n+11=limnx1n+1⎜ ⎜x1n(n+1)1⎟ ⎟n2=limnx1n+1.x1n(n+1)11n(n+1).n2n(n+1)=1.logex.1=logex
Hence, option 'C' is correct.

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