Question

1/2*3 + 1/3*4 + ... +1/49*50

Answer 1

1/2×3 + 1/3×4 + ... + 1/49×50

= 1/2 - 1/3 + 1/3 - 1/4 + ... +1/49 - 1/ 50

=  1/2 - 1/50

=12/25

Answer 2

\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

\(=\frac{1}{2}-\frac{1}{50}=\frac{24}{50}=\frac{12}{25}\)