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Question

The value of nr=1log(arbr1) is

A
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C
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Solution

The correct option is C

The given series is
loga+log(a2b)+log(a3b2)+log(a4b3)+............+log(anbn1)
This is an A.P. with first term loga and the common difference
log(a2b)loga=log(ab)
Therefore the sum of n terms is
n2 [ loga+log(anbn1)] = n2log (an+1bn1)
​ Trick : Check for n=1,2.


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