a(2n-1) = 1/5^(2n-1),
a(2n) = -2/5^(2n),
a(2n-1) + a(2n) = 1/5^(2n-1) - 2/5^(2n) = 5/5^(2n) - 2/5^(2n) = 3/5^(2n) = 3/(25)^n
= (3/25)[1/(25)^(n-1)],
s(n) = a(1)+a(2)+...+a(2n-1)+a(2n)
= (3/25)[1 + 1/25 + 1/(25)^2 + ...+ 1/(25)^(n-1)]
= (3/25)[ 1- 1/(25)^n]/[1-1/25]
= (1/8)[1 - 1/(25)^n]
lim_{n-> 无穷}s(n) = lim_{n->无穷}(1/8)[ 1- 1/(25)^n] = 1/8