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1-1/2+1/3-1/4+.+1/50
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1-1/2+1/3-1/4+.+1/50
▼优质解答
答案和解析
1-1/2+1/3-1/4+……+（1/2n-1）-1/2n
=1+1/2+1/3+1/4+……+（1/2n-1）+1/2n
-2(1/2+1/4+1/6+1/8+...+1/2n)
=1+1/2+1/3+1/4+……+（1/2n-1）+1/2n
-(1/1+1/2+1/3+1/4+...+1/n-1+1/n)
即：抵消了前n项,剩下的是后n项是从1/（n+1）至1/2n
=1/(n+1)+1/(n+2)+1/(n+3)+...+1/(2n-1)+1/2n
1-1/2+1/3-1/4+.+1/50=1/26+1/27+1/28+.+1/50
=1+1/2+1/3+1/4+……+（1/2n-1）+1/2n
-2(1/2+1/4+1/6+1/8+...+1/2n)
=1+1/2+1/3+1/4+……+（1/2n-1）+1/2n
-(1/1+1/2+1/3+1/4+...+1/n-1+1/n)
即：抵消了前n项,剩下的是后n项是从1/（n+1）至1/2n
=1/(n+1)+1/(n+2)+1/(n+3)+...+1/(2n-1)+1/2n
1-1/2+1/3-1/4+.+1/50=1/26+1/27+1/28+.+1/50
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