find the long-run value for each sequence:
U0 = 45
Un = (1 - 0.05) Un -1 + 5
and the other problem is:
Find the long-run value for each sequence:
U0 = 12
Un = 0.9 Un-1 + 2
2006-09-24 04:42:29 · 4 answers · asked by poetic_lala 5 in Science & Mathematics ➔ Mathematics
For the first one: [n→∞]lim U_n = 100
For the second: [n→∞]lim U_n = 20
Method: if these sequences converge at all (which they do) then the value given for U_n should always be closer to the limit than U_(n-1). Thus logically, if you were to put in the value of the limit for U_(n-1), then the value you get for U_n should be equal to it. Therefore, you can find the limit by simply assuming that U_n=U_(n-1) and solving. I'll replace both variables with x to make the math simpler:
x=(1-0.05)x+5
x=.95x+5
.05x=5
x=100
The solution for the second problem is similar.
2006-09-24 06:42:53 · answer #1 · answered by Pascal 7 · 0⤊ 0⤋
u0=45
u1=(1-0.05) 45+5
=47.75
u2=(1-0.05)u1+5
=50.3625
...
do the second in same way.
2006-09-24 11:57:03 · answer #2 · answered by iyiogrenci 6 · 0⤊ 0⤋
Us solving your math problems won't help you
2006-09-24 11:45:14 · answer #3 · answered by Anonymous · 0⤊ 0⤋
that looks hard...I aint got a clue ...sorry :-S
2006-09-24 11:45:21 · answer #4 · answered by ♥♥♥GODDESS♥♥♥ 5 · 0⤊ 0⤋