Question

Tính hợp lí nếu có thể

A= 5/1.4+ 5/4.7+ 5/7.10+...+5/ 307.310

làm ơn giúp mk mk sẽ đời đời nhớ ơn

Answer 1

Có : 3/5 A = 3/1.4 + 3/4.7 + 3/7.10 + ..... + 3/307.310

= 1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ........ + 1/307 - 1/310

= 1 - 1/310

= 309/310

=> A = 309/310 : 3/5 = 103/62

Tk mk nha

Answer 2

        \(\frac{5}{1.4}+\frac{5}{4.7}+\frac{5}{7.10}+...+\frac{5}{307.310}\)

\(=\frac{5}{3}\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{307.310}\right)\)

\(=\frac{5}{3}\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{307}-\frac{1}{310}\right)\)

\(=\frac{5}{3}\left(1-\frac{1}{310}\right)\)

\(=\frac{5}{3}.\frac{309}{310}=\frac{103}{62}\)

Answer 3

A=(5/1-5/4+5/4-5/7+...+5/307-5/310):3

A=(5/1-5/310):3

A=103/62

Answer 4

\(\frac{5}{1.4}+\frac{5}{4.7}+\frac{5}{7.10}+...+\frac{5}{307.310}\)

\(=\frac{5}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{307.310}\right)\)

\(=\frac{5}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{307}+\frac{1}{310}\right)\)

\(=\frac{5}{3}.\left(1-\frac{1}{310}\right)\)

\(=\frac{5}{3}.\frac{309}{310}=\frac{103}{62}\)