提问一道高中数学题。
4个回答
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a1=2, a2=1
an/a(n+1) + an/a(n-1) =2
an/a(n+1) - 1= -[an/a(n-1) -1]
=> {an/a(n-1) -1} 是等比数列, q=-1
an/a(n-1) -1 = (-1)^(n-1). (a2/a1 -1)
=(1/2) . (-1)^n
an/a(n-1) = 1+ (1/2) . (-1)^n
a2/a1 = 3/2 (1)
a3/a2= 1/2 (2)
a4/a3 = 3/2 (3)
...
...
a11/a10 = 1/2 (10)
a12/a11 =3/2 (11)
(1)*(2)*(3)*....*(11)
a12/a1 = (3/2)^5 . (1/2)^4
= 243/512
a12= (243/512). a1
=243/256
an/a(n+1) + an/a(n-1) =2
an/a(n+1) - 1= -[an/a(n-1) -1]
=> {an/a(n-1) -1} 是等比数列, q=-1
an/a(n-1) -1 = (-1)^(n-1). (a2/a1 -1)
=(1/2) . (-1)^n
an/a(n-1) = 1+ (1/2) . (-1)^n
a2/a1 = 3/2 (1)
a3/a2= 1/2 (2)
a4/a3 = 3/2 (3)
...
...
a11/a10 = 1/2 (10)
a12/a11 =3/2 (11)
(1)*(2)*(3)*....*(11)
a12/a1 = (3/2)^5 . (1/2)^4
= 243/512
a12= (243/512). a1
=243/256
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