Câu 1:

\(C=\dfrac{15}{1\times4}+\dfrac{15}{2\times5}+\dfrac{15}{3\times6}+...+\dfrac{15}{47\times50}\)

\(\dfrac{3}{15}C=\dfrac{3}{1\times4}+\dfrac{3}{2\times5}+\dfrac{3}{3\times6}+...+\dfrac{3}{47\times50}\)

\(=1-\dfrac{1}{4}+\dfrac{1}{2}-\dfrac{1}{5}+\dfrac{1}{3}-\dfrac{1}{6}+...+\dfrac{1}{47}-\dfrac{1}{50}\)

\(=\left(1+\dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{47}\right)-\left(\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{1}{6}+...+\dfrac{1}{50}\right)\)

\(=1+\dfrac{1}{2}+\dfrac{1}{3}-\left(\dfrac{1}{48}+\dfrac{1}{49}+\dfrac{1}{50}\right)\)

Câu này chỉ biết làm tới đây thôi.

Câu 2:

\(M=\dfrac{5}{7\times9}+\dfrac{5}{9\times11}+\dfrac{5}{11\times13}+...+\dfrac{5}{89\times91}\)

\(\dfrac{2}{5}M=\dfrac{2}{7\times9}+\dfrac{2}{9\times11}+\dfrac{2}{11\times13}+...+\dfrac{2}{89\times91}\) \(\dfrac{2}{5}M=\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}+...+\dfrac{1}{89}-\dfrac{1}{91}\) \(\dfrac{2}{5}M=\dfrac{1}{7}-\dfrac{1}{91}\)

\(\dfrac{2}{5}M=\dfrac{12}{91}\)

\(M=\dfrac{12}{91}\div\dfrac{2}{5}\)

\(M=\dfrac{30}{91}\)