![](https://rs.olm.vn/images/avt/0.png?1311)
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)
5/2+13/6+25/12+41/20+61/30+85/42
=2+1/2+2+1/6+2+1/12+2+1/20+2+1/30+2+1/42
=12+(1/2+1/6+1/12+1/20+1/30+1/42)
=12+(1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7)
=12+(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7)
=12+1-1/7
=90/7
5/2+13/6+25/12+41/20+61/30+85/42
=2+1/2+2+1/6+2+1/12+2+1/20+2+1/30+2+1/42
=12+(1/2+1/6+1/12+1/20+1/30+1/42)
=12+(1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+1/6.7)
=12+(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7)
=12+1-1/7
=90/7
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)
\(=1-\frac{1}{6}+1-\frac{1}{12}+...+1-\frac{1}{90}\)
\(=\left(1+1+1+...+1\right)-\left(\frac{1}{6}+\frac{1}{12}+...+\frac{1}{90}\right)\)
\(=\left(1+1+1+...+1\right)-\left(\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{9\cdot10}\right)\)
Từ 2 đến 9 có : ( 9 - 2 ) / 1 + 1 = 8 ( số hạng ) => có 8 số 1
\(\Rightarrow8-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=8-\left(\frac{1}{2}-\frac{1}{10}\right)\)
\(=8-\frac{2}{5}=\frac{38}{5}\)
b) \(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+...+\frac{109}{110}\)
\(=1-\frac{1}{2}+1-\frac{1}{6}+...+1-\frac{1}{110}\)
\(=\left(1+1+1+...+1\right)-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{110}\right)\)
\(=\left(1+1+...+1\right)-\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{10\cdot11}\right)\)
Từ 1 đến 10 có : ( 10 - 1 ) / 1 + 1 = 10 ( số hạng ) => có 10 số 1
\(\Rightarrow10-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10}-\frac{1}{11}\right)\)
\(=10-\left(1-\frac{1}{11}\right)\)
\(=10-\frac{10}{11}=\frac{100}{11}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
9 - A = 1 - 1/2 + 1-5/6 + 1 - 11/12 + ... + 1-89/90
9 - A = 1/2 + 1/6 + 1/12 + .. + 1/90
9 - A = 1/1.2 + 1/2.3 + 1/3.4 + .. + 1/9.10
9-A = 1/1 - 1/2 + 1/2 - 1/3 + ... + 1/9 - 1/10
9 -A = 1/1 - 1/10
9 - A = 9/10
A = 9 - 9/10
A = 81/10
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có
\(B=\frac{1}{2}+\frac{1}{6}+................+\frac{1}{90}=\frac{1}{1x2}+.....+\frac{1}{9x10}=1-\frac{1}{2}+...+\frac{1}{9}-\frac{1}{10}=\frac{9}{10}\)
Dễ thấy B+A=1+1+...+1=10
=>A=10-B=\(10-\frac{9}{10}=\frac{91}{10}\)
\(A=\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+....+\frac{89}{90}\)
\(A=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{12}\right)+..+\left(1-\frac{1}{90}\right)\)
\(A=\left(1-\frac{1}{1.2}\right)+\left(1-\frac{1}{2.3}\right)+\left(1-\frac{1}{3.4}\right)+...+\left(1-\frac{1}{9.10}\right)\)
\(A=\left(1+1+1+...+1\right)+\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)
9 số 1
\(A=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(A=9-\left(1-\frac{1}{10}\right)\)
\(A=9-\frac{9}{10}\)
\(A=\frac{81}{10}\)
Ủng hộ mk nha ^-^
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=\frac{1}{2}+\frac{5}{6}+...+\frac{89}{90}\)
\(A=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+...+\left(1-\frac{1}{90}\right)\)
\(A=9-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{90}\right)\)
Gọi \(A=9-B\)
\(B=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{9\cdot10}\)
\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\)
\(B=1-\frac{1}{10}=\frac{9}{10}\)
\(A=9-\frac{9}{10}\)
\(A=\frac{90-9}{10}=\frac{81}{10}\)
Ko đúng hơi tiếc :D
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu hỏi của Try Build Gundam - Toán lớp 7 - Học toán với OnlineMath
\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+...+\frac{89}{90}\)
\(=1-\frac{1}{2}+1-\frac{1}{6}+1-\frac{1}{12}+1-\frac{1}{20}+...+1-\frac{1}{90}\)
\(=9-\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)
\(=9-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)
\(=9-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{9}-\frac{1}{10}\right)\)
\(=9-\left(1-\frac{1}{10}\right)\)
\(=9-\frac{9}{10}=\frac{81}{10}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu hỏi của Nguyễn Ngọc Mai Anh - Toán lớp 5 - Học toán với OnlineMath
\(\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\)\(\frac{55}{66}\)\(+\frac{71}{72}\)\(+\frac{89}{90}\)
\(=1-\frac{1}{2}+1-\frac{1}{6}+...+1-\frac{1}{90}\)
\(=9-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{90}\right)\)
\(=9-\left(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{9.10}\right)\)
\(=9-\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-....+\frac{1}{9}-\frac{1}{10}\right)\)
\(=9-\left(1-\frac{1}{10}\right)\)
\(=8+\frac{1}{10}=\frac{81}{10}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{1}{12}\right)+...+\left(1-\dfrac{1}{90}\right)\\ =\left(1+1+1+1+1+1+1+1+1\right)-\left(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{90}\right)\\ =9-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{9\cdot10}\right)\\ =9-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ =9-\left(1-\dfrac{1}{10}\right)=9-\dfrac{9}{10}=\dfrac{81}{10}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1/2+5/6+11/12+19/20+29/30+41/42+55/56+71/72+89/90 =
1-1/2+1-1/6+1-1/12+1-1/20+1-1/30+1-1/42+1-1/56+1-1/72+1-1/90 =
9 – (1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90) =
9 – [1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+1/(5x6)+1/(6x7)+1/(7x8)+1/(8x9)+1/(9x10)] =
9 – ( 1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10) =
9 – (1 – 1/10) = 9 – 9/10 = 81/10
\(A=\dfrac{5}{2}+\dfrac{14}{6}+\dfrac{25}{12}+\dfrac{41}{20}+\dfrac{61}{30}+\dfrac{85}{42}+\dfrac{113}{56}+\dfrac{145}{72}+\dfrac{181}{90}\)
\(A=\dfrac{29}{6}+\dfrac{25}{12}+\dfrac{41}{20}+\dfrac{61}{30}+\dfrac{85}{42}+\dfrac{113}{56}+\dfrac{145}{72}+\dfrac{181}{90}\)
\(A=\dfrac{83}{12}+\dfrac{41}{20}+\dfrac{61}{30}+\dfrac{85}{42}+\dfrac{113}{56}+\dfrac{145}{72}+\dfrac{181}{90}\)
\(A=\dfrac{269}{30}+\dfrac{61}{30}+\dfrac{85}{42}+\dfrac{113}{56}+\dfrac{145}{72}+\dfrac{181}{90}\)
\(A=11+\dfrac{85}{42}+\dfrac{113}{56}+\dfrac{145}{72}+\dfrac{181}{90}\)
\(A=\dfrac{547}{42}+\dfrac{113}{56}+\dfrac{145}{72}+\dfrac{181}{90}\)
\(A=\dfrac{361}{24}+\dfrac{145}{72}+\dfrac{181}{90}\)
\(A=\dfrac{307}{18}+\dfrac{181}{90}\)
\(A=\dfrac{286}{15}\)