Question

Let `f(k)= k/2009` and `g(k) = (f^4(k))/[(1-f(k))^4+(f(k))^4]` then the sum `sum_(k=0)^2009 g(k)` is equal?

Answer 1

`1005`

Explanation:

Calling `k_(max)=2009` we have

`sum_(k=0)^(k_(max)) k^4/((c-k)^4+k^4) = sum_(k=0)^((k_(max)-1)/2)( k^4/((k_(max)-k)^4+k^4)+ (k_(max)-k)^4/(k^4+(k_(max)-k)^4))=(k_(max)-1)/2+1 = 1005`