Question

\(\dfrac{2}{1\times2\times3}+\dfrac{2}{2\times3\times4}+\dfrac{2}{3\times4\times5}+...+\dfrac{2}{48\times49\times50}\)

Answer 1

\(\dfrac{2}{1\times2\times3}+\dfrac{2}{2\times3\times4}+\dfrac{2}{3\times4\times5}+...+\dfrac{2}{48\times49\times50}\)

\(=\dfrac{1}{1\times2}-\dfrac{1}{2\times3}+\dfrac{1}{2\times3}-\dfrac{1}{3\times4}+\dfrac{1}{3\times4}-\dfrac{1}{4\times5}+...+\dfrac{1}{48\times49}-\dfrac{1}{49\times50}\)

\(=\dfrac{1}{1\times2}-\dfrac{1}{49\times50}\)

\(=\dfrac{1}{2}-\dfrac{1}{2450}\)

\(=\dfrac{612}{1225}\)

\(\text{#}Toru\)

Answer 2

1/2 - 1/49 x50