Not a "normal" question

Calculus Level 3

Sketch the probability density function of a normal distribution with some mean and standard deviation. Call this graph f ( x ) f(x) .

Define g ( n ) = g(n)= number of turning points f ( n ) ( x ) f^{(n)}(x) has, where f ( n ) ( x ) f^{(n)}(x) is the n t h n^{th} derivative of f ( x ) f(x) .

What is the value of ∑ n = 0 20 g ( n ) \sum_{n=0}^{20} g(n) ?

BONUS: can you generalise this for ∑ n = 0 k g ( n ) \sum_{n=0}^{k} g(n) ?


The answer is 231.

Jihoon Kang by Jihoon Kang , 24, United Kingdom

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