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# If is defined for all nonnegative integers b by b = (b + 1)^b, what

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Re: If is defined for all nonnegative integers b by b = (b + 1)^b, what [#permalink]
Danou
Bunuel
guddo
If ▲ is defined for all nonnegative integers b by $$▲b = (b + 1)^b$$, what is the value of ▲(▲(▲0)) ?

A. 0
B. 2
C. 3
D. 4
E. 9

Attachment:
2024-01-27_16-38-36.png

Since $$▲b = (b + 1)^b$$, then:

$$▲0 = (0 + 1)^0 = 1^0 = 1$$;

$$▲(▲0) = ▲1 = (1 + 1)^1 = 2^1 = 2$$;

$$▲(▲(▲0)) = ▲2 = (2 + 1)^2 = 3^2 = 9$$.

­
I am not sure I understand. What is the significance of the triangle?
­
▲ represents a function, which is defined for all nonnegative integers b by $$▲b = (b + 1)^b$$.

For example:
If b = 0, then $$▲0 = (0 + 1)^0=1$$;
If b = 1, then $$▲1 = (1 + 1)^1=2$$;
If b = 2, then $$▲2 = (2 + 1)^2=9$$;
If b = 3, then $$▲3 = (3 + 1)^3=64$$;
...

13. Functions

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