Its good to be consecutive

Calculus Level 2

a ( a − 1 ) > ( a − 1 ) a \large a^{(a-1)}>(a-1)^a

Find the sum of all positive integers a a that satisfy the inequality above.

14 5 2 9 6 10

Nihar Mahajan by Nihar Mahajan , 20, India

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1 solution

I tried to solve it mathematically, I got stuck at

a > a a ( a − 1 ) a > \sqrt[a]{a} (a-1)

Then I proceeded to guessing the solutions; because after guessing 5 randomly, the inequality wasn't satisfied, so the solutions are definitely less than 5

So the solutions were: 1,2,3, and the sum is 6

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