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Question

The value of nr=1log(arbr1) is

A
n2log(anbn)
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B
n2log(anbn+1)
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C
n2log(an+1bn+1)
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D
n2log(an+1bn1)
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Solution

The correct option is D n2log(an+1bn1)
Now,
nr=1log(arbr1)
=nr=1(logarlogbr1)
=nr=1(rloga(r1)logb)
=(loga)×n(n+1)2logb×(n1)n2
=n2(logan+1logbn1)
=n2log(an+1bn1)

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