66Lets make it more general:
Let f(x)=\dfrac{a^x}{a^x+\sqrt{a}} for some positive a.
Find the sum:
\sum_{k=1}^nf\left(\dfrac{k}{n}\right)
Consider two cases: Case I: n is even, and Case II: n is odd.
Let f(x) = 4x4x+2. What is the value of
\sum_{1}^{1000}{f\frac{i}{1000}}
Source: Chinese: 1986
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66