SOLUTION: The general term of Un of a series is defined by the relation Un+1=0.3*(1+Un). n is greater than or equal to 1 and U1 =1. Calculate U2, U3 and U4. A second series is defined with

Question 1107203: The general term of Un of a series is defined by the relation Un+1=0.3*(1+Un). n is greater than or equal to 1 and U1 =1. Calculate U2, U3 and U4.
A second series is defined with the general term Vn, by the relation Vn=Un - 0.5 n is greater than or equal to 1.
Show that this series(Vn) is an exponential series.
Express Vn and hence Un as function of n.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The general term of Un of a series is defined by the relation Un+1=0.3*(1+Un). n is greater than or equal to 1 and U1 =1.
Calculate
U2 = 0.3(1+1) = 0.6
U3 = 0.3(1.6) = 0.48
U4 = 0.3(1.48 = 0.444
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A second series is defined with the general term Vn, by the relation Vn=Un - 0.5 n is greater than or equal to 1.
Show that this series(Vn) is an exponential series.
V1 = U(1)-0.5
V2 = [U(1)-0.5]2 = 2U(1)-1
V3 = [2U(1)-1]3 = 6U(1)-3
I see no exponentiation.
Cheers,
Stan H.
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Express Vn and hence Un as function of n.
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