Inspired by Satyajit Mohanty

Calculus Level 5

$1-\frac { 1 }{ 2 } +\frac { 1 }{ 3 } -\frac { 1 }{ 5 } +\frac { 1 }{ 6 } -\frac { 1 }{ 7 } +\frac { 1 }{ 9 } -\frac { 1 }{ 10 } +\frac { 1 }{ 11 } -\frac { 1 }{ 13 } +\frac { 1 }{ 14 } -\frac { 1 }{ 15 } +\frac { 1 }{ 17 } -\dots$ 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.

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