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Question

limn(1n+1+1n+2+.....+12n)=

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Solution

Now,
limn(1n+1+1n+2+.....+12n)
=limn1n⎜ ⎜ ⎜11+1n+11+2n+.....+11+nn⎟ ⎟ ⎟
=limnnr=11n⎜ ⎜11+rn⎟ ⎟
=1011+x dx [ Using definition of definite integral]
=|log|(1+x)||x=1x=0
=log2.

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