Writo's Arithmetic Progression

Calculus Level 3

If \(a_1, a_2, \cdots a_{4001}\) are in Arithmetic Progression

and \[\frac{1}{a_1 a_2} + \frac{1}{a_2 a_3} + \cdots + \frac{1}{a_{4000} a_{4001}} = 10 \]

and \[a_2 + a_{4000} = 50\]

Evaluate \[ | a_1 - a_{4001} | \]

Thanks to @Writo for this problem
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