SOLUTION: a1 = 24^1/3, an+1=(an+24)^1/3, n ≥ 1. Then the integer part of a100 equals A. 2 B. 10 C. 100 D. 24

Question 872658: a1 = 24^1/3, an+1=(an+24)^1/3, n ≥ 1. Then the integer part of a100 equals
A. 2
B. 10
C. 100
D. 24

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
<--->
So meaning that is true for
Could it be true for all positive integer values.
If it were true for , we would know that .
Then

,
and since and ,
we conclude that .
Since is true for ,
and being true for makes it true for ,
then is true for all values of .
The integer part of for any is ,
and so the integer part of is .
It is true that gets ever closer to , but it can never get there.
RELATED QUESTIONS
Write the equation of the arithmetic sequence defined by a1 = 3 and a4 = 0. (write your (answered by stanbon)

X Y 15 N 18 8 1/3 24 6... (answered by Fombitz)

Choose the recursive formula for the sequence 7, �1, �9, �17, ... Then choose the next... (answered by Alan3354)

24, Use the four digits given below to create an expression that equals 24, using only... (answered by ankor@dixie-net.com)

Which of the following could be an exact value of n^4 where n is an integer? A. 1.6 x... (answered by josgarithmetic,Theo,MathLover1)

What is the "nth" term of this sequence? a1=2 1/2, d=1 1/2,... (answered by Fombitz)

-7/10 = 2 2/5d A. -1 7/10 B. -3 1/10 C. -7/24 D. -1... (answered by rfer)

If n is any positive odd integer greater than 1, the n(n^2 � 1) is always divisible by: (answered by richwmiller)

``write the first six terms of the sequence 2. an=(n+1)^3 4. an=n/n+3 write the... (answered by CubeyThePenguin)

SOLUTION: a1 = 24^1/3, an+1=(an+24)^1/3, n &#8805; 1. Then the integer part of a100 equals A. 2 B. 10 C. 100 D. 24

SOLUTION: a1 = 24^1/3, an+1=(an+24)^1/3, n ≥ 1. Then the integer part of a100 equals A. 2 B. 10 C. 100 D. 24