a) A = 3/10.12 + 3/12.14 + ... + 3/998.1000
2/3.A = 2/10.12 + 2/12.14 + ... + 2/998.1000
2/3.A = 1/10 - 1/12 + 1/12 - 1/14 + ... + 1/998 - 1/1000
2/3.A = 1/10 - 1/1000
2/3.A = 99/1000
A = 99/1000 : 2/3
A = 99/1000 . 3/2
A = 297/2000
b) B = 2/1.4 + 2/4.7 + 2/7.10 + ... + 2/22.25
3/2.B = 3/1.4 + 3/4.7 + 3/7.10 + ... + 3/22.25
3/2.B = 1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/22 - 1/25
3/2.B = 1 - 1/25
3/2.B = 24/25
B = 24/25 : 3/2
B = 24/25 . 2/3
B = 16/25
Ủng hộ mk nha ^_-
a) Ta có: \(A=\frac{3}{10.12}+\frac{3}{12.14}+....+\frac{3}{998.1000}.\)
\(\Rightarrow\frac{2}{3}A=\frac{1}{10.12}+\frac{1}{12.14}+...+\frac{1}{998.1000}\)
\(\Rightarrow\frac{2}{3}A=\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+...+\frac{1}{998}-\frac{1}{1000}\)
\(\Rightarrow\frac{2}{3}A=\frac{1}{10}-\frac{1}{1000}=\frac{99}{1000}\)
\(\Rightarrow A=\frac{99}{1000}:\frac{2}{3}=\frac{297}{2000}\)
Ta có: \(B=\frac{2}{1.4}+\frac{2}{4.7}+...+\frac{2}{22.25}\)
\(\Rightarrow\frac{3}{2}B=\frac{1}{1.4}+\frac{1}{4.7}+...+\frac{1}{22.25}\)
\(\Rightarrow\frac{3}{2}B=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{22}-\frac{1}{25}\)
\(\Rightarrow\frac{3}{2}B=1-\frac{1}{25}=\frac{24}{25}\)
\(\Rightarrow B=\frac{24}{25}:\frac{3}{2}=\frac{16}{25}\)
\(A=\frac{3}{10.12}+\frac{3}{12.14}+\frac{3}{14.16}+.....+\frac{3}{998.1000}\)
\(=\frac{3}{2}.\left(\frac{2}{10.12}+\frac{2}{12.14}+...+\frac{2}{998.1000}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}+....+\frac{1}{998}-\frac{1}{1000}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{10}-\frac{1}{1000}\right)\)
\(=\frac{3}{2}.\frac{99}{1000}\)
\(=\frac{297}{2000}\)
a) A = 3/10.12 + 3/12.14 + ... + 3/998.1000
2/3.A = 2/10.12 + 2/12.14 + ... + 2/998.1000
2/3.A = 1/10 - 1/12 + 1/12 - 1/14 + ... + 1/998 - 1/1000
2/3.A = 1/10 - 1/1000
2/3.A = 99/1000
A = 99/1000 : 2/3
A = 99/1000 . 3/2
A = 297/2000
b) B = 2/1.4 + 2/4.7 + 2/7.10 + ... + 2/22.25
3/2.B = 3/1.4 + 3/4.7 + 3/7.10 + ... + 3/22.25
3/2.B = 1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/22 - 1/25
3/2.B = 1 - 1/25
3/2.B = 24/25
B = 24/25 : 3/2
B = 24/25 . 2/3
B = 16/25
