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Question

limnn[1(n+1)(n+2)+1(n+2)(n+4)++16n2] is equal to

A
log(32)
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B
log(52)
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C
log(12)
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D
log(74)
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Solution

The correct option is A log(32)
Let L=limnn[1(n+1)(n+2)+1(n+2)(n+4)++16n2]
=limnnnr=11(n+r)(n+2r)
=limnnn21r=11(1+rn)(1+2rn)
=limn1n1r=11(1+rn)(1+2rn)
=10dx(1+x)(1+2x)=10(11+x+21+2x)dx
=[log(1+x)+log(1+2x)]10
=[log2+log3(log1+log1)]=log(32)

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