S= 1/2 - 1/2 + 1/3 - 1/3 + 1/4 - 1/4 +...+ 1/50 - 1/50
S= 0 + 0 + 0 +...+ 0
S= 0
\(S=\frac{1}{2.2}+\frac{1}{3.3}+\frac{1}{4.4}+...+\frac{1}{49.49}+\frac{1}{50.50}\)
\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{3}-\frac{1}{3}+...+\frac{1}{50}-\frac{1}{50}\)
\(=0+0+...+0\)
\(=0\)