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a)\(\frac{4}{3.7}+\frac{4}{7.11}+...+\frac{4}{23.27}=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{23}-\frac{1}{27}=\frac{1}{3}-\frac{1}{27}=\frac{8}{27}\)
b)\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{6.7}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)
c)\(\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}+\frac{2}{1.2}+\frac{2}{2.3}+...+\frac{2}{9.10}=\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{11}-\frac{1}{13}\right)+2\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=\frac{1}{3}-\frac{1}{13}+2\left(1-\frac{1}{10}\right)=\frac{10}{39}+\frac{9}{5}=\frac{401}{195}\)
a) 3/2:9/4+21/8
= 3/2 x 4/9 + 21/8
=12/18 + 21/8
= 2/3 + 21/8 = 16/24 + 63/24 = 79/24
b) 3/10+5/2x1/3
=3/10 + 5/6
= 9/30 + 25/30 = 34/30 = 17/15
c) 8/15:3/11+2/15:2/11
= 8/15x11/3 + 2/15x11/2
= 88/45 + 22/30
= 88/45 + 11/15 = 88/45 + 33/45 = 121/45
d) 19/5-11/4:9/8
= 19/5 - 11/4x8/9
= 19/5 - 88/36
= 19/5 - 22/9 = 171/45 - 110/45 = 61/45
e) 33/7:11/6+37/15x21/74
= 33/7x6/11 + 7/10
= 198/77 + 7/10 = 1980/770 + 1386/770 = 153/35
a) 3/2:9/4+21/8
= 3/2 x 4/9 + 21/8
=12/18 + 21/8
= 2/3 + 21/8 = 16/24 + 63/24 = 79/24
b) 3/10+5/2x1/3
=3/10 + 5/6
= 9/30 + 25/30 = 34/30 = 17/15
c) 8/15:3/11+2/15:2/11
= 8/15x11/3 + 2/15x11/2
= 88/45 + 22/30
= 88/45 + 11/15 = 88/45 + 33/45 = 121/45
d) 19/5-11/4:9/8
= 19/5 - 11/4x8/9
= 19/5 - 88/36
= 19/5 - 22/9 = 171/45 - 110/45 = 61/45
e) 33/7:11/6+37/15x21/74
= 33/7x6/11 + 7/10
= 198/77 + 7/10 = 1980/770 + 1386/770 = 153/35
a) \(\frac{1.3+3.5+5.7+7.9}{3.6+9.10+15.14+21.18}\)
= \(\frac{1.3+3.5+5.7+7.9}{1.3.2.3+3.5.2.3+5.7.2.3+7.9.2.3}\)
= \(\frac{1.3+3.5+5.7+7.9}{1.3.6+3.5.6+5.7.6+7.9.6}\)
= \(\frac{1.3+3.5+5.7+7.9}{6.\left(1.3+3.5+5.7+7.9\right)}=\frac{1}{6}\)
Dấu "." là dấu nhân cấp 2
b) \(\frac{1.2+2.3+3.4+4.5}{3.6+6.9+9.12+12.15}\)
= \(\frac{1.2+2.3+3.4+4.5}{1.2.3.3+2.3.3.3+3.4.3.3+4.5.3.3}\)
= \(\frac{1.2+2.3+3.4+4.5}{1.2.9+2.3.9+3.4.9+4.5.9}\)
= \(\frac{1.2+2.3+3.4+4.5}{9.\left(1.2+2.3+3.4+4.5\right)}=\frac{1}{9}\)
Dấu "." là dấu nhân cấp 2
c) \(\frac{0,3+\frac{3}{7}+\frac{3}{11}}{0,4+\frac{4}{7}+\frac{4}{11}}\)= \(\frac{\frac{3}{10}+\frac{3}{7}+\frac{3}{11}}{\frac{4}{10}+\frac{4}{7}+\frac{4}{11}}\)= \(\frac{3.\left(\frac{1}{10}+\frac{1}{7}+\frac{1}{11}\right)}{4.\left(\frac{1}{10}+\frac{1}{7}+\frac{1}{11}\right)}=\frac{3}{4}\)
a)\(2-3+5-7+9-11+13-15+17=\left(2+5+9+13+17\right)-\left(3+7+11+15\right)\)
\(=46-36=10\)
b)\(\frac{1}{1.2}+\frac{1}{2.3}+...............+\frac{1}{8.9}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.................+\frac{1}{8}-\frac{1}{9}\)
\(=\frac{1}{1}-\frac{1}{9}=\frac{9}{9}-\frac{1}{9}=\frac{8}{9}\)
Áp dụng \(\frac{1}{n.\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)
Chúc bạn học tốt
Đề là tính bằng cách hợp lý đúng ko bạn
a, 2-3+5-7+9-11+13-15+17
= (5+13) - (3+15) + (2+9-11) + (17-7)
= 18 - 18 + 0 +10
= 10
b, \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)
\(=1-\frac{1}{9}\)
\(=\frac{8}{9}\)
1/2 + 1/3 + 1/4 = 6/12 + 4/12 + 3/12 = 13/12
2/3 + 3/4 + 4/5 = 8/12 + 9/12 + 4/5 = 17/12 + 4/5 = 85 / 60 + 48 / 60 = 133/ 60
6/5 + 4/3 + 7/9 = 18/ 15 + 20/15 + 7/9 = 38 /15 + 7/ 9 = 114/45 +35/45 = 149/45
8/9 - 5/6 = 16/18 - 15/18 = 1/18
15/17 - 11 /13 = 195/221 -187/221= 8/221
a) \(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\)
= \(\frac{6}{12}+\frac{4}{12}+\frac{3}{12}\)
= \(\frac{13}{12}\).
b) \(\frac{2}{3}+\frac{3}{4}+\frac{4}{5}\)
= \(\frac{8}{12}+\frac{9}{12}+\frac{4}{5}\)
= \(\frac{17}{12}+\frac{4}{5}\)
= \(\frac{85}{60}+\frac{48}{60}\)
= \(\frac{133}{60}\).
c)\(\frac{6}{5}+\frac{4}{3}+\frac{7}{9}\)
= \(\frac{54}{45}+\frac{62}{45}+\frac{35}{45}\)
= \(\frac{151}{45}\).
d) \(\frac{8}{9}-\frac{5}{6}\)
= \(\frac{16}{18}-\frac{15}{18}\)
= \(\frac{1}{18}\).
e) \(\frac{15}{17}-\frac{11}{13}\)
= \(\frac{195}{221}\)\(-\frac{187}{221}\)
= \(\frac{8}{221}\).
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10=55
2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20=110
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19=100
k mk nha pạn hiền!
10 +1 = 11 có 10 số vậy thì 10 : 2 = 5 thì sẽ bằng 5x11 = 55
2 + 20 = 22 cũng có 10 số lấy 10 : 2 = 5 se bang 22 x5 = 110
1+19 = 20 , 10 : 2 = 5 , 20x5 = 100
\(\frac{3-\frac{3}{2}+\frac{3}{4}}{5-\frac{5}{2}+\frac{5}{4}}:\frac{6-\frac{6}{9}+\frac{6}{11}}{15-\frac{15}{9}+\frac{15}{11}}\)
\(=\frac{3\left(1-\frac{1}{2}+\frac{1}{4}\right)}{5\left(1-\frac{1}{2}+\frac{1}{4}\right)}:\frac{6\left(1-\frac{1}{9}+\frac{1}{11}\right)}{15\left(1-\frac{1}{9}+\frac{1}{11}\right)}\)
\(=\frac{3}{5}:\frac{6}{15}\)
\(=\frac{3}{5}:\frac{2}{5}=\frac{3}{5}\cdot\frac{5}{2}=\frac{3}{2}\)
3-3/2+3/4 =3x(1-1/2+1/4)
5-5/2+5/4 5x(1-1/2-1/4
rút gọn đi (1-1/2+1/4) là chỉ còn 3/5
câu dưới tương tự, kết quả là 6/15=2/5