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.
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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