1.A sequence U1,U2,U3,.... is defined by U1=10, Un+1=0.9Un *[Un+1 ge n+1都係右下ge.1唔係1個數..]
a,find the value of U4
∞
b. find Σ Ur
r=1
Geometric progression and the Binomial expansion
2007-03-04 5:31 am
回答 (2)
2007-03-04 6:01 am
✔ 最佳答案
A sequence U1,U2,U3,.... is defined by U1=10, Un+1=0.9Un (a) Find the value of U4
∞
(b) Find Σ Ur.
r=1
(a)
Obviously, Un=(0.9n-1)10
Then U4=(0.9³)10=7.29
(b)
∞
Σ Ur.
r=1
=10+0.9(10)+0.9²(10)+......
=10/(1-0.9)
=100
2007-03-04 6:03 am
此是一公比q=0.9的等比數列,可利用公式
U4=U1*q^3
=10*0.729=7.29
∞
Σ Ur=U1/(1-q)=10/0.1=100
r=1
U4=U1*q^3
=10*0.729=7.29
∞
Σ Ur=U1/(1-q)=10/0.1=100
r=1
收錄日期: 2021-04-12 14:32:24
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