For my Friend Kushagra Sahni! 20 Dec

Algebra Level 3

$\large a<{ \left( 1+\frac { 1 }{ n } \right) }^{ n }<b$

If above inequality is true for all positive integers $n,$ then what positive integers $a$ and $b$ minimize the quantity $|b - a|?$ Give your answer as $a+b.$

The answer is 4.

1 solution

Reynan Henry
Dec 20, 2015

A < e < b. So a=2 and b=3

With $n=1$ , we get that $a < 2$ . Hence we cannot have $a = 2$ .

The answer should be $a = 1, b = 3$ , for a total of 4.

I have updated the answer to 4.

Calvin Lin Staff - 5 years, 5 months ago

For my Friend Kushagra Sahni! 20 Dec

The answer is 4.

1 solution

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