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If A(k)=(k+1)^k, and k=0, what is the value of A(A(A(k)))?

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If A(k)=(k+1)^k, and k=0, what is the value of A(A(A(k)))?

by Max@Math Revolution » Mon Feb 29, 2016 7:41 pm
If A(k)=(k+1)^k, and k=0, what is the value of A(A(A(k)))?

A. 0
B. 2
C. 4
D. 6
E. 9


* A solution will be posted in two days.
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by Brent@GMATPrepNow » Tue Mar 01, 2016 2:36 pm
Max@Math Revolution wrote:If A(k) = (k+1)^k, and k = 0, what is the value of A(A(A(k)))?

A. 0
B. 2
C. 4
D. 6
E. 9
We want A(A(A(0)))

Start with the innermost nested bracket:
A(0) = (0 + 1)^0 = 1^0 = 1

Great. Now we have: A(A(1))
A(1) = (1 + 1)^1 = 2^1 = 2

Now we have: A(2)
A(2) = (2 + 1)^2 = 3^2 = 9

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Wed Mar 02, 2016 9:48 pm
If A(k)=(k+1)^k, and k=0, what is the value of A(A(A(k)))?

A. 0
B. 2
C. 4
D. 6
E. 9


-> A(A(A(0)))=A(A(1))=A(2)=(2+1)^2=9.
Thus, the answer is E.
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