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Calculus Level 5

Find the value of:

\[\sum _{ k=1 }^{ \infty }{ \frac { 1 }{ k\left( 1+12k \right) } } \]

The answer is of the form:

\[A-B\left( ln2+\frac { ln3 }{ C } \right) -\pi \left( D+\frac { \sqrt { E } }{ F } \right) +G\sqrt { H } ln\left( \sqrt { I-\sqrt { J } } \right) \]

Find the value of: \(A+B+C+D+E+F+G+H+I+J\)

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