数学必修五的1已知等差数列 {an}满足:a3=7,a3+a7=26(1)求通项公式an及前N项和sn;(2)令bn=1
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数学必修五的
1已知等差数列 {an}满足:a3=7,a3+a7=26
(1)求通项公式an及前N项和sn;
(2)令bn=1/a²n-1(n∈正整数),求数列{bn}的前n项和Tn
1已知等差数列 {an}满足:a3=7,a3+a7=26
(1)求通项公式an及前N项和sn;
(2)令bn=1/a²n-1(n∈正整数),求数列{bn}的前n项和Tn
1 a7=26-a3=26-7=19
d=(a7-a3)/(7-3)=3
a1=a3-2d=7-2*3=1
an=2n-2 Sn=n*1+{n*(n-1)/2}*3
2 bn=1/{(an+1)(an-1)}=1/{(2n-1)(2n-3)}
用裂项求和算Tn
Tn=-0.5(1+1)-0.5(1/3-1)-0.5(1/5-1/3)-.-0.5{1/(2n-1)-1/(2n-3)}
=-0.5{1+1/(2n-1)}
d=(a7-a3)/(7-3)=3
a1=a3-2d=7-2*3=1
an=2n-2 Sn=n*1+{n*(n-1)/2}*3
2 bn=1/{(an+1)(an-1)}=1/{(2n-1)(2n-3)}
用裂项求和算Tn
Tn=-0.5(1+1)-0.5(1/3-1)-0.5(1/5-1/3)-.-0.5{1/(2n-1)-1/(2n-3)}
=-0.5{1+1/(2n-1)}
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