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?

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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?

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Answer 1 · 2017-03-05T16:42:34

#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#

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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?

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