Question

Tính nhanh

\(\frac{3}{1\cdot3}+\frac{3}{3\cdot5}+\frac{3}{5\cdot7}+...+\frac{3}{99\cdot100}\)

Giúp mk với T.T

Answer 1

Bạn viết đề sai rồi, mình sửa đề nhé, bài này ngắn lắm =((

\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{99.101}\)

\(=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=\frac{3}{2}\left(1-\frac{1}{101}\right)=\frac{3}{2}.\frac{100}{101}=\frac{150}{101}\)(rút gọn phân số)

Answer 2

Ta có : 

\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{99.101}\) ( sai đề rồi ) 

\(=\)\(\frac{3}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{99.101}\right)\)

\(=\)\(\frac{3}{2}\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\right)\)

\(=\)\(\frac{3}{2}\left(1-\frac{1}{101}\right)\)

\(=\)\(\frac{3}{2}.\frac{100}{101}\)

\(=\)\(\frac{150}{101}\)

Vậy \(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{99.101}=\frac{150}{101}\)

Chúc bạn học tốt ~ 

Answer 3

0 có sai đề đâu

đề thi mk đó

Answer 4

\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+...+\frac{3}{99.100}\)

\(=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1+\left(-\frac{1}{3}+\frac{1}{3}\right)+\left(-\frac{1}{5}+\frac{1}{5}\right)+\left(-\frac{1}{7}+\frac{1}{7}\right)+...+\left(-\frac{1}{99}+\frac{1}{99}\right)-\frac{1}{100}\)

\(=1+0+0+0+...+0-\frac{1}{100}\)

\(=1-\frac{1}{100}=\frac{99}{100}\)

Answer 5

\(\frac{3}{1.3}+\frac{3}{3.5}+...+\frac{3}{99.101}\)

\(=\frac{3}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{99.101}\right)\)

\(=\frac{3}{2}\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...-\frac{1}{99}+\frac{1}{99}-\frac{1}{101}\right)\)

\(=\frac{3}{2}\left(1-\frac{1}{101}\right)=\frac{3}{2}.\frac{100}{101}=\frac{150}{101}\)