>>548
S(n) の定義から
a(1) = S(1) = -25
a(n) = S(n)-S(n-1) = (n^2) -26n -{ (n-1)^2 -26(n-1)} = 2n-27

a(2) = S(2)-S(1) = -23

a(n) = 2n -27 > 0
n > 27/2 となる最小のnは 14

Σ_{n=1 to 50} |a(n)| = -a(1)-a(2)-…-a(13) + a(14) + … + a(50)
= S(50) - 2 S(13) = 1538