11No takers???
Ques) If f1(x) = (x/2) + 10 , for all x belonging to R and defined by f n (x) = f1 { fn-1 (x)}, for all n≥2. Then show that lim n →∞ fn(x) = 20
I try to solve it this way,
f1(x) = x/2 + 10 = (x+20) /2
Similarily, f2(x)=. (x+60) /4
f3(x) = (x+140) / 8
f4(x) = (x+300) / 16
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The denominator(2,4,8,16,....) is forming a G.P of r=2
BUT STILL IN VAIN
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6 Answers
1We can use here that condition ..
as the n is tending to infinity ...
f (n ) = f ( n +1 ) = f (n-1 ) .. just see if it could help .. !
1357it is ofcourse right
from your solution
f1=(x+20)/2
f2=(x+60)/4=(x+80-20)/4=x/4+20-20/4
f3=(x+140)/8=(x+160-20)/8=x/8+20-20/23
f4(x)=x/24+20-20/24
Now continue from here, you will get the result