Question

Tính tổng:

3/1*3 + 3/3*5 + 3/5*7 + ... + 3/49*51

giúp mình nhé các bn ^-^

Answer 1

\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{49.51}\)

\(=3.\left(\frac{1}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{49.51}\right)\)

\(=3.\frac{1}{3}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right)\)

\(=\frac{3}{3}\left(1-\frac{1}{51}\right)\)

\(=\frac{50}{51}\)

Answer 2

thanks bạn nha

Answer 3

\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{49.51}\)

\(=\frac{3}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right)\)

\(=\frac{3}{2}.\left(1-\frac{1}{51}\right)\)

\(=\frac{3}{2}.\frac{50}{51}=\frac{25}{17}\)