作业帮高二数列第二问,
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高二数列第二问,
(1)
L:{(x,y)| y=2x+1 }
Pn(an,bn)
x=0
y=1
P1=(0,1)
an = a1+(n-1)
= n-1
bn = 2an +1
= 2(n-1) +1
= 2n-1
(2)
|P1Pn|^2 = (bn -1 )^2 + (an)^2
= (2n-2)^2 + (n-1)^2
= 5(n-1)^2
|P1Pn| =√5(n-1)
cn =√5/[n.|P1Pn|]
= 1/[(n-1)n]
= 1/(n-1) -1/n
lim(n-> ∞) (c2+c3+...+cn)
=lim(n-> ∞) [ 1 - 1/n]
= 1
L:{(x,y)| y=2x+1 }
Pn(an,bn)
x=0
y=1
P1=(0,1)
an = a1+(n-1)
= n-1
bn = 2an +1
= 2(n-1) +1
= 2n-1
(2)
|P1Pn|^2 = (bn -1 )^2 + (an)^2
= (2n-2)^2 + (n-1)^2
= 5(n-1)^2
|P1Pn| =√5(n-1)
cn =√5/[n.|P1Pn|]
= 1/[(n-1)n]
= 1/(n-1) -1/n
lim(n-> ∞) (c2+c3+...+cn)
=lim(n-> ∞) [ 1 - 1/n]
= 1