g=1.3^2+3.5^2+5.7^2+...+97.99^2
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
2/1.3 + 2/3.5 + 2/5.7 +...+ 2/97.99
=(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+...+(1/97-1/99)
=1-1/99=98/99
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{97.99}\)
\(A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{97}-\frac{1}{99}\)
\(A=\frac{1}{1}-\frac{1}{99}\)
\(A=\frac{98}{99}\)
ta có A=1-1/3+1/2-1/5+..................1/95-1/97+1/97-1/99
A=1-1/99
A=98/99
![](https://rs.olm.vn/images/avt/0.png?1311)
\(B=\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+\dfrac{2}{5\cdot7}+...+\dfrac{2}{97\cdot99}+\dfrac{2}{99\cdot101}\\ B=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}+\dfrac{1}{99}-\dfrac{1}{101}\\ B=\dfrac{1}{1}-\dfrac{1}{101}\\ B=\dfrac{101}{101}-\dfrac{1}{101}\\ B=\dfrac{100}{101}\)
\(\dfrac{2}{1\cdot3}=\dfrac{1}{1}-\dfrac{1}{3}=\dfrac{3}{3}-\dfrac{1}{3}=\dfrac{2}{3}\)
\(\dfrac{2}{3\cdot5}=\dfrac{1}{3}-\dfrac{1}{5}=\dfrac{5}{15}-\dfrac{3}{15}=\dfrac{2}{15}\)
\(\dfrac{2}{5\cdot7}=\dfrac{1}{5}-\dfrac{1}{7}=\dfrac{7}{35}-\dfrac{5}{35}=\dfrac{2}{35}\)
và cứ như thế đến số cuối
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
=3.(3/1.3+3/3.5+3/5.7+...+3/95.97+3/97.99)
=3(1-1/3+1/3-1/5+1/5-1/7+...+1/95-1/97+1/97-1/99)
=3[(1-1/99)+(1/5-1/5)+(1/7-1/7)+...+(1/97-1/97)]
=3(1-1/99)=3(99/99-1/99)=3.98/99=1.98/33=98/33
![](https://rs.olm.vn/images/avt/0.png?1311)
A=1.3.(5-2)+3.5.(7-2)+5.7.(9-2)+...+97.99(101-2)=
=(1.3.5+3.5.7+5.7.9+...+97.99.101) - 2.(1.3+3.5+5.7+...+97.99)
Đặt
B=1.3.5+3.5.7+5.7.9+...+97.99.101
=> 8B=1.3.5.8+3.5.7.8+5.7.9.8+...+97.99.101.8=
=1.3.5(7+1)+3.5.7.(9-1)+5.7.9.(11-3)+...+97.99.101.(103-95)=
=1.3.5+1.3.5.7-1.3.5.7+3.5.7.9-3.5.7.9+5.7.9.11-...-95.97.99.101+97.99.101.103=
=3.5+97.99.101.103
\(\Rightarrow B=\dfrac{15+97.99.101.103}{8}\)
Đặt
C=1.3+3.5+5.7+...+97.99
=> 6C=1.3.6+3.5.6+5.7.6+...+97.99.6=
=1.3.(5+1)+3.5.(7-1)+5.7.(9-3)+...+97.99.(101-95)=
=1.3+1.3.5-1.3.5+3.5.7-3.5.7+5.7.9-...-95.97.99+97.99.101=
=1.3+97.99.101
\(\Rightarrow C=\dfrac{3+97.99.101}{6}\)
\(\Rightarrow A=B-2C\)
Thay các giá trị của B và C bạn tự tính nốt nhé
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+.....+\)\(\frac{2}{97.99}\)
\(A=2\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+.........+\frac{1}{97.99}\right)\)
\(A=2\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{97}-\frac{1}{99}\right)\)
\(A=2\left(\frac{1}{1}-\frac{1}{99}\right)\)
\(A=2.\frac{98}{99}\)
\(A=\frac{196}{99}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
ko bt nha