求n趋向无穷时 [(1+1/n)(1+2/n)...(1+n/n)]^1/n 的极限?

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求n趋向无穷时[(1+1/n)(1+2/n)...(1+n/n)]^1/n的极限?求n趋向无穷时[(1+1/n)(1+2/n)...(1+n/n)]^1/n的极限?求n趋向无穷时[(1+1/n)(1+

求n趋向无穷时 [(1+1/n)(1+2/n)...(1+n/n)]^1/n 的极限?
求n趋向无穷时 [(1+1/n)(1+2/n)...(1+n/n)]^1/n 的极限?

求n趋向无穷时 [(1+1/n)(1+2/n)...(1+n/n)]^1/n 的极限?
设T=lim(n->∞)[(1+1/n)(1+2/n)...(1+n/n)]^1/n
∵lnT=ln{[(1+1/n)(1+2/n)...(1+n/n)]^1/n}=∫(0,1)ln(1+x)dx (由定积分定义得)
=2ln2-1=ln(4/e)
∴T=4/e
故原式=4/e.