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Question: Answered & Verified by Expert
If $n=(1999) !$, then $\sum_{x=1}^{1999} \log _{n} x$ is equal to
MathematicsSequences and SeriesVITEEEVITEEE 2013
Options:
  • A 1
  • B 0
  • C $\sqrt[1999]{1999}$
  • D $-1$
Solution:
2547 Upvotes Verified Answer
The correct answer is: 1
$\sum_{x=1}^{1999} \log _{n} x$
$=\log _{(1999) !} 1+\log _{(1999) !} 2+\ldots+\log _{(1999) !} 1999$
$=\log _{(1999) !}(1.2 .3 \ldots 1999)$
$=\log _{(1999) !}(1999) !=1$

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