...是公差为d(d>0)的等差数列,Sn为{an}的前n项和,已知S4=24,a2乘a3...
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发布时间:2024-10-23 20:47
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热心网友
时间:2024-11-06 00:38
(1)S4=a1+a2+a3+a4=2(a2+a3)=24,
a2+a3=12
a2a3=35.解得a2=5,a3=7或者a2=7,a3=5(舍去,因为d>0)
所以d=2,a1=3
an=3+(n-1)*2=2n+1
bn=1/[ana(n+1)]=1/(2n+1)(2n+3)=[1/(2n+1)-1/(2n+3)]*(1/2)
Tn=b1+b2+b3+b4+……+bn=(1/2)*[1/3-1/5+1/5-1/7+……-1/(2n+3)]=(1/2)[1/3-1/(2n+3)]=n/(6n+9)
热心网友
时间:2024-11-06 00:40
(1)S4=2(a2+a3),a2+a3=12
a2a3=35
t^2-12t+35=0
a2=5,a3=7
an=2n+1
(2)1/an(an+1)=(1/2)[1/(2n+1)-1/(2n+3)]
Tn=1/2(1/3-1/5+1/5-1/7+...-1/(2n+1)+1/(2n+1)-1/(2n+3))
=n/[3(2n+3)]