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Question

limπ[n!nn]1n equals [Kurukshetra CEE 1998]


  1. e
  2. 1/e


Solution

The correct option is C

1/e


Let P=limx(n!nn)1n=limx(1n.2n.3n.4nnn)1n
logP=1nlimπ(log1n+log2n++lognn)
log Plimxnr=11n log rn
log P=10 log x dx=(x log xx)10=(1)P=1e

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