\(\frac{5}{5.7}+\frac{5}{7.9}+...+\frac{5}{59.61}\)

\(=\frac{5}{2}\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)

\(=\frac{5}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\right)\)

\(=\frac{5}{2}\left(\frac{1}{5}-\frac{1}{61}\right)=\frac{5}{2}.\frac{56}{305}=\frac{28}{61}\)

ko co de]

\(\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}+...+\frac{3}{59.61}\) 

\(=\)\(\frac{3}{2}\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+...+\frac{2}{59.61}\right)\)

\(=\)\(\frac{3}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{59}-\frac{1}{61}\right)\)

\(=\)\(\frac{3}{2}\left(\frac{1}{5}-\frac{1}{61}\right)\)

\(=\)\(\frac{3}{2}.\frac{56}{305}\)

\(=\)\(\frac{84}{305}\)

Chúc bạn học tốt ~ 

\(\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{59.61}\)

\(=\frac{3}{2}.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)

\(=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\right)\)

\(=\frac{3}{2}.\left(\frac{1}{5}-\frac{1}{61}\right)\)

\(=\frac{3}{2}.\left(\frac{61}{305}-\frac{5}{305}\right)\)

\(=\frac{3}{2}.\frac{56}{305}\)

\(=\frac{84}{305}\)

\(S=\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{20}}\)

\(\Rightarrow2S=1+\frac{1}{2}+...+\frac{1}{2^{19}}\)

\(\Rightarrow2S-S=1-\frac{1}{2^{20}}\)

\(\Rightarrow S=1-\frac{1}{2^{20}}\)

Chúc bạn học tốt !!! 

\(=\frac{4}{5.7}+\frac{4}{7.9}+\frac{4}{9.11}+...+\frac{4}{59.61}\)

\(=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)

\(=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{59}-\frac{1}{61}\right)\)

=\(2.\left(\frac{1}{5}-\frac{1}{61}\right)\)

\(=2.\left(\frac{36}{505}\right)\)

\(=\frac{72}{505}\)

TK nha !!

Ta có : \(\frac{4}{5.7}+\frac{4}{7.9}+\frac{4}{9.11}+....+\frac{4}{59.61}\)

\(=2\left(\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+.....+\frac{2}{59.61}\right)\)

\(=2\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{59}-\frac{1}{61}\right)\)

\(=2\left(\frac{1}{5}-\frac{1}{61}\right)\)

\(=2.\frac{56}{305}=\frac{112}{305}\)

Mk nhân lộn ở cái phần \(2.\left(\frac{1}{5}-\frac{1}{61}\right)\)

\(=2.\left(\frac{56}{305}\right)\)

\(=\frac{112}{305}\)

Tk nha cảm ơn !!

toán 1 sao?

\(\frac{3}{5\cdot7}+\frac{3}{7\cdot9}+...+\frac{5}{53\cdot55}\)

\(=\frac{3}{2}\cdot\left(\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{53\cdot55}\right)\)

\(=\frac{3}{2}\cdot\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{53}-\frac{1}{55}\right)\)

\(=\frac{3}{2}\cdot\left(\frac{1}{5}-\frac{1}{55}\right)\)

\(=\frac{3}{2}\cdot\left(\frac{11}{55}-\frac{1}{55}\right)\)

\(=\frac{3}{2}\cdot\frac{10}{55}\)

\(=\frac{3}{2}\cdot\frac{2}{11}\)

\(=\frac{3}{11}\)

đây mà là lớp 1 ak 

\(\frac{4}{1\cdot3\cdot5}+\frac{4}{3\cdot5\cdot7}+\frac{4}{5\cdot7\cdot9}+\frac{4}{7\cdot9\cdot11}+\frac{4}{9\cdot11\cdot13}\)

\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{9.11}-\frac{1}{11.13}\)

\(=\frac{1}{1.3}-\frac{1}{11.13}\)

\(=\frac{1}{3}-\frac{1}{143}\)

\(=\frac{140}{429}\)

đặt \(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{97.99}\) là A

A = \(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{97.99}\)

2A = 2 . (\(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{97.99}\))

2A = \(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{97.99}\)

2A = \(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\)

2A = \(\frac{1}{3}-\frac{1}{99}\)

2A = \(\frac{33}{99}-\frac{1}{99}\)

2A = \(\frac{32}{99}\)

A = \(\frac{32}{99}:2\)

A = \(\frac{32}{99}.\frac{1}{2}\)

A = \(\frac{32}{198}\)

A = \(\frac{16}{99}\)

HỌC TỐT

a.\(\frac{3\cdot4\cdot7}{12\cdot8\cdot9}\)= \(\frac{3\cdot4\cdot7}{3\cdot4\cdot8\cdot9}\)= \(\frac{7}{72}\) 

b. \(\frac{4\cdot5\cdot6}{12\cdot10\cdot8}\)= \(\frac{4\cdot5\cdot2\cdot3}{3\cdot4\cdot5\cdot2\cdot8}\)= \(\frac{1}{8}\) 

c.\(\frac{5\cdot6\cdot7}{12\cdot14\cdot15}\)= \(\frac{5\cdot6\cdot7}{2\cdot6\cdot2\cdot7\cdot3\cdot5}\)= \(\frac{1}{12}\)

1) \(A=\frac{4}{5.7}+\frac{4}{7.9}+...+\frac{4}{59.61}\)

\(A=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)

\(A=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+..+\frac{1}{59}-\frac{1}{61}\right)\)

tiếp theo bạn tính kết quả trong ngoặc rồi nhân với 2 là ra kết quả của phần 1

phần 2 tách 3^2 = 3.3 sau đó lấy thừa số chung là 3,tiếp theo làm như phần 1 là ra kết quả

chưa bao giờ nghĩ là toán 6

B=2²(\(\frac{2}{3.5}\)+\(\frac{2}{5.7}\)+\(\frac{2}{7.9}\)+...+\(\frac{2}{101.103}\))

B=4[1/3-1/5+1/5-1/7+1/7-1/9 +...+1/101-1/103]

B=4[1/3-1/103]

B=4.(100/309)

B=400/309

MOI NGUOI NHO K VA KET BAN VOI MINH NHE