\[1-\frac { 1 }{ 2 } +\frac { 1 }{ 3 } -\frac { 1 }{ 5 } +\frac { 1 }{ 6 } -\frac { 1 }{ 7 } +\frac { 1 }{ 9 } -\frac { 1 }{ 10 } +\frac { 1 }{ 11 } -\frac { 1 }{ 13 } +\frac { 1 }{ 14 } -\frac { 1 }{ 15 } +\frac { 1 }{ 17 } -\dots\]
If the above expression can be expressed as \[\dfrac { (A\sqrt { B } -C){ \pi }^{ D } }{ E }\] for positive integers \(A,B,C,D \) and \(E\). Find the minimum value of \(A\times B \times C \times D \times E\)

Inspired by
Problem 1, Problem 2, Problem 3.