作业帮如图,手机党悲剧
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/27 09:49:35
如图,手机党悲剧
如图,手机党悲剧
如图,手机党悲剧
因为Sn=1+1/n^2+1/(n+1)^2=(n^4+2n^3+3n^2+2n+1)/(n^2*(n+1)^2)=(n*(n+1)+1)^2/(n^2*(n+1)^2)
所以√Sn=√(n*(n+1)+1)^2/(n^2*(n+1)^2)=[n(n+1)+1]/[n(n+1)]
所以S=3/2+7/6+13/12+...+[n(n+1)+1]/[n(n+1)]=(1+1/2)+(...
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因为Sn=1+1/n^2+1/(n+1)^2=(n^4+2n^3+3n^2+2n+1)/(n^2*(n+1)^2)=(n*(n+1)+1)^2/(n^2*(n+1)^2)
所以√Sn=√(n*(n+1)+1)^2/(n^2*(n+1)^2)=[n(n+1)+1]/[n(n+1)]
所以S=3/2+7/6+13/12+...+[n(n+1)+1]/[n(n+1)]=(1+1/2)+(1+1/6)+...+(1+1/(n(n+1)))=n+[1/2+1/6+...+1/(n(n+1))]=n+[(1-1/2)+(1/2-1/3)+...+(1/n-1/(n+1))]=n+1-1/(n+1)
n^2就是n的平方的意思哈，特此备注，怕你看不懂
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（n²+2n）/（n+1）
必对，我初三，刚做过过程算出√s1=3/2 √s2=7/6 √s3=13/12 设 n分别等于 1 2 3 …… 则 将√s1=3/2 √s2=7/6 √s3=13/12 …… 分别加起来 分别等于 3/2 8/3 15/4 ...
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（n²+2n）/（n+1）
必对，我初三，刚做过
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s1=1+1/1^2+1/2^2=9/4
根号s1=3/2=1+[1/(1*2)]
s2=1+1/2^2+1/3^2=49/36
根号s2=7/6=1+[1/(2^3)]
sn=1+1/n^2+1/(n+1)^2=[(n^2+n+1)/(n^2+n)]^2
根号sn=(n^2+n+1)/(n*2+n)=1+[1+1/(n^2+n)]=1+1/n*(n+1)<...
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s1=1+1/1^2+1/2^2=9/4
根号s1=3/2=1+[1/(1*2)]
s2=1+1/2^2+1/3^2=49/36
根号s2=7/6=1+[1/(2^3)]
sn=1+1/n^2+1/(n+1)^2=[(n^2+n+1)/(n^2+n)]^2
根号sn=(n^2+n+1)/(n*2+n)=1+[1+1/(n^2+n)]=1+1/n*(n+1)
s=根号s1+根号s2+......+根号sn
=n*1+[1/(1*2)+1/(2*3)+,,,,,,,+1/n*(n+1))]
=n+{1+1/2-1/2+1/3-1/3-,,,,,,1/(n+1)]}
=n+[1-1/(n+1)]
=(n+1)-1/(n+1)
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