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已知数列a(n)是等差数列,且a1=2,a1+a2+a3=12.求1/s1+1/s2+1/s3+...+1/s10的值
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已知数列a(n)是等差数列,且a1=2,a1+a2+a3=12.求1/s1+1/s2+1/s3+...+1/s10的值
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答案和解析
a1=2,a1+a2+a3=3a1+3d=12
d=2
sn=na1+(n-1)nd/2=n^2+n=n(n+1)
1/s1+1/s2+1/s3+...+1/s10
=1/(1x2)+1/(2x3)+1/(3x4)+.1/(10x11)
=1-1/2+1/2-1/3+1/3-1/4.+1/10-1/11
=1-1/11
=10/11
d=2
sn=na1+(n-1)nd/2=n^2+n=n(n+1)
1/s1+1/s2+1/s3+...+1/s10
=1/(1x2)+1/(2x3)+1/(3x4)+.1/(10x11)
=1-1/2+1/2-1/3+1/3-1/4.+1/10-1/11
=1-1/11
=10/11
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