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Calculate the value of the sum
\sum_{k=1}^{9999999} \frac{1}{(k+1)^{3/2} + (k^2-1)^{1/3} + (k-1)^{2/3}}.
\sum_{k=1}^{9999999} \frac{1}{(k+1)^{3/2} + (k^2-1)^{1/3} + (k-1)^{2/3}}.
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