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11+113+23+113+23+33+113+23+33+43+… \frac 1 1 + \frac 1 {1^3 + 2^3}+ \frac 1 {1^3 + 2^3 + 3^3 }+ \frac 1 {1^3 + 2^3 + 3^3 +4^3 } + \ldots 11+13+231+13+23+331+13+23+33+431+…
If the series above can be expressed as aπ2b−c \frac {a \pi^2}{b} - c baπ2−c for positive integers a,b,ca,b,ca,b,c with a,ba,ba,b coprime. Find a+b+ca+b+ca+b+c.
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