设首项为3,公差为2的等差数列,其前n项和为sn,求数列{1/sn}的前n项和Tn.
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设首项为3,公差为2的等差数列,其前n项和为sn,求数列{1/sn}的前n项和Tn.
![设首项为3,公差为2的等差数列,其前n项和为sn,求数列{1/sn}的前n项和Tn.](/uploads/image/z/6966054-54-4.jpg?t=%E8%AE%BE%E9%A6%96%E9%A1%B9%E4%B8%BA3%2C%E5%85%AC%E5%B7%AE%E4%B8%BA2%E7%9A%84%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E5%85%B6%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BAsn%2C%E6%B1%82%E6%95%B0%E5%88%97%7B1%2Fsn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CTn.)
an=1+2n,
sn=(a1+an)/2 n=(3+1+2n)/2 *n=n(n+2),
1/sn =1/n(n+2) =1/2 *(1/n-1/(n+2)),
Tn=1/2{1+1/2-1/(n+1)-1/(n+2)}=3/4-1/2*【1/(n+1)+1/(n+2)】
sn=(a1+an)/2 n=(3+1+2n)/2 *n=n(n+2),
1/sn =1/n(n+2) =1/2 *(1/n-1/(n+2)),
Tn=1/2{1+1/2-1/(n+1)-1/(n+2)}=3/4-1/2*【1/(n+1)+1/(n+2)】
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