Summation of Function 2016

Algebra Level 3

Let f ( x ) = 3 x 2 − 3 x + 1 f(x) = 3x^2-3x+ 1 . Find

[ f ( 1 ) + f ( 2 ) + f ( 3 ) + ⋯ + f ( 2016 ) ] m o d 1 0 4 . [ f(1) +f(2) + f(3) + \cdots + f(2016) ] \bmod{10^4}.


The answer is 96.

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Choi Chakfung by choi chakfung , 28, Hong Kong

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1 solution

It's just the summation of 3 x 2 − 3 x + 1 3x^2-3x+1 from 1 to 2016

It's important to recall that the summation of x^2 from 1 to n is n ( n + 1 ) ( 2 n + 1 ) / 6 n(n+1)(2n+1)/6 And the summation of x from 1 to n is n ( n + 1 ) / 6 n(n+1)/6

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