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? Calculus Introduction to Calculus What is Calculus? 1 Answer Cesareo R. Mar 5, 2017 #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# Answer link Related questions How can calculus be applied to real life? How can calculus be used in economics? How can calculus be used to optimize manufacturing processes? How does calculus different from algebra? How does calculus relate to business? How does calculus relate to chemistry? How does calculus relate to computer science? How does calculus relate to medicine? How does calculus relate to physics? Who invented Calculus? See all questions in What is Calculus? Impact of this question 3593 views around the world You can reuse this answer Creative Commons License