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等差数列An的首项为a1等于3公差等于2前n项和为Sn求数列.1/Sn的前n项和Tn

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等差数列An的首项为a1等于3公差等于2前n项和为Sn求数列.1/Sn的前n项和Tn
等差数列An的首项为a1等于3公差等于2前n项和为Sn求数列.1/Sn的前n项和Tn
a1=3 d=2
Sn=[2*3+2(n-1)]*n/2=n(n+2)
1/Sn=(1/2)[1/n-1/(n+2)]
Tn=(1/2)[(1-1/3)+(1/2-1/4)+(1/3-1/5)+.+1/n-1/(n+2)]
=(1/2)[1+1/2-1/(n+1)-1/(n+2)]
=(1/2)[3/2-(2n+3)/(n+1)(n+2)]
=n(3n-5)/[4(n+1)(n+2)]
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