作业帮lim n→∞[1/(n+1)+1/(n+2)+…+1/(n+n)]=?求极值!
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lim n→∞[1/(n+1)+1/(n+2)+…+1/(n+n)]=?求极值!
lim [1/(n+1)+1/(n+2)+…+1/(n+n)]=?
n→∞
lim [1/(n+1)+1/(n+2)+…+1/(n+n)]=?
n→∞
lim(n→∞) [1/(n+1)+1/(n+2)+…+1/(n+n)]
=lim(n→∞) 1/n * [1/(1+1/n)+1/(1+2/n)+…+1/(1+n/n)]
=lim(n→∞) 1/n *Σ1/(1+i/n)
由定积分的定义,
lim(n→∞) 1/n *Σ1/(1+i/n)
=∫(0到1) 1/(1+x) dx
=ln|1+x| 代入上下限1和0
=ln2 -ln1
=ln2
=lim(n→∞) 1/n * [1/(1+1/n)+1/(1+2/n)+…+1/(1+n/n)]
=lim(n→∞) 1/n *Σ1/(1+i/n)
由定积分的定义,
lim(n→∞) 1/n *Σ1/(1+i/n)
=∫(0到1) 1/(1+x) dx
=ln|1+x| 代入上下限1和0
=ln2 -ln1
=ln2
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