Question

Tính

B = \(\frac{3}{1.2.3}+\frac{3}{2.3.4}+...+\frac{3}{49.50.51}\)

Answer 1

\(B=\frac{3}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{49.50.51}\right)\)

\(=\frac{3}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{49.50}-\frac{1}{50.51}\right)\)

\(=\frac{3}{2}\left(\frac{1}{2}-\frac{1}{2550}\right)\)

\(=\frac{3}{2}\cdot\frac{637}{1275}\)

\(=\frac{637}{850}\)

Answer 2

mk trả lời câu này rồi đó

Answer 3

nhân B với 3/2 r` rút gọn

Answer 4

\(B=\frac{3}{1.2.3}+\frac{3}{2.3.4}+...+\frac{3}{49.50.51}\)

\(B=\frac{3}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{49.50.51}\right)\)

\(B=\frac{3}{2}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.5}+...+\frac{1}{49.50}-\frac{1}{50.51}\right)\)

\(\Rightarrow B=\frac{3}{2}.\left(\frac{1}{1.2}-\frac{1}{50.51}\right)\)

\(\Rightarrow B=\frac{3}{2}.\left(\frac{1}{2}-\frac{1}{2550}\right)\)

\(\Rightarrow B=\frac{3}{2}.\frac{637}{1275}\)

\(\Rightarrow B=\frac{1911}{2550}\)