Function Series

Algebra Level pending

Given f ( x ) f(x) = x 2 x^{2} . Calculate f ( 10 ) + f ( 20 ) + f ( 30 ) + f ( 40 ) + f ( 50 ) + . . . f ( 10000 ) f(10)+f(20)+f(30)+f(40)+f(50)+...f(10000) .


The answer is 33383350000.

Jovan Alfian Djaja by Jovan Alfian Djaja , 18, Indonesia

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1 solution

f ( 10 ) + f ( 20 ) + . . + f ( 10000 ) f(10)+f(20)+..+f(10000) = 100 + 400 + .... 100,000,000 

                                      = 100 (1 + 4 + 9 + 16 + ... + 1,000,000)

Notice that the series in bracket is the series of quadratic numbers. By using the formula, we have: 

                                      = 100 (333833500) =33383350000
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