求证:1-1/2+1/3-1/4+1/5-1/6+……+1/(2n-1)=1/(n+1)+1/(n+2)+……+1/2n
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求证:1-1/2+1/3-1/4+1/5-1/6+……+1/(2n-1)=1/(n+1)+1/(n+2)+……+1/2n(n∈)
当n=>∞时
S=ln2
1-1/2+1/3-1/4……+1/2n
=1+1/2+1/3+1/4……+1/2n-2(1/2+1/4+……+1/2n)
=1/(n+1)+1/(n+2)+……1/2n
=1/n(1/(1+1/n)+1/(1+2/n)+……+1/(1+n/n)
=1/(1+x)[从0积到1]=ln2
满意请采纳.
S=ln2
1-1/2+1/3-1/4……+1/2n
=1+1/2+1/3+1/4……+1/2n-2(1/2+1/4+……+1/2n)
=1/(n+1)+1/(n+2)+……1/2n
=1/n(1/(1+1/n)+1/(1+2/n)+……+1/(1+n/n)
=1/(1+x)[从0积到1]=ln2
满意请采纳.
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