高三数学数列题
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an=a1+(n-1)d
(I)
S5=30
5(a1+2d)=30
a1+2d=6 (1)
a1.a9=(a3)^2
a1(a1+8d)=(a1+2d)^2
(6-2d)(6+6d)=36
(3-d)(1+d)=3
-d^2+2d=0
d=2
from (1)
a1+4=6
a1=2
an = 2+2(n-1) = 2n
(II)
Sn =n(n+1)
bn
= a(n-1).a(n+2)/Sn
= 4(n-1)(n+2)/[n(n+1)]
=4- 8/[n(n+1)]
=4- 8[1/n-1/(n+1)]
b2+b3+...+bn
=4(n-1) -8[ 1/2 - 1/(n+1) ]
=4(n-1) -4 + 1/(n+1)
=4(n-2) + 1/(n+1)
(I)
S5=30
5(a1+2d)=30
a1+2d=6 (1)
a1.a9=(a3)^2
a1(a1+8d)=(a1+2d)^2
(6-2d)(6+6d)=36
(3-d)(1+d)=3
-d^2+2d=0
d=2
from (1)
a1+4=6
a1=2
an = 2+2(n-1) = 2n
(II)
Sn =n(n+1)
bn
= a(n-1).a(n+2)/Sn
= 4(n-1)(n+2)/[n(n+1)]
=4- 8/[n(n+1)]
=4- 8[1/n-1/(n+1)]
b2+b3+...+bn
=4(n-1) -8[ 1/2 - 1/(n+1) ]
=4(n-1) -4 + 1/(n+1)
=4(n-2) + 1/(n+1)
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