An algebra problem by William Whitehouse

Algebra Level pending

If $a,b$ and $c$ are real numbers such that $a+b+c=n$ , what is the largest value of $a^{b^{c}}$ in terms of $n$ ?

n-1

n

The maximum value exists only for values of

n<1

The maximum value only exists for values of

n\leq 1

The maximum value does not exist A limit exists for all

n

but there is no closed form for it

1 solution

William Whitehouse
Feb 23, 2017

let a=m+n-1 ,b=1 , c=-m where m is an arbitrarily large number the expression becomes m+n-1 and since m can be arbitrarily large so can the expression.

An algebra problem by William Whitehouse

1 solution

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