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Question

If L=limnnn2[(n+1)(n+12)(n+122)(n+12n1)]n, then the value of lnL is 


Solution

limnnn2[(n+1)(n+12)(n+122)(n+12n1)]n

=limn⎢ ⎢ ⎢ ⎢(n+1)(n+12)(n+122)(n+12n1)nn⎥ ⎥ ⎥ ⎥n

=limn[(1+1n)n(1+12n)n(1+122n)n(1+12n1n)n]

=e1e1/2e1/22e1/2n1 upto 

=e1+1/2+1/22+

=e2

Mathematics

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