\(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11}\)

\(=\frac{1}{2}\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{11}\right)\)

\(=\frac{1}{2}\cdot\frac{10}{11}=\frac{5}{11}\)

B=1/4x (7+9) + 1/5x(9+11) + 1/6x(11+13) + 1/7x13

=4+2+4+\(\frac{13}{7}\)=10+\(\frac{13}{7}\)=\(\frac{83}{7}\)

\(a,3\dfrac{4}{5}+2\dfrac{1}{5}=\dfrac{19}{5}+\dfrac{11}{5}=\dfrac{30}{5}=6\\ b,7\dfrac{2}{9}-2\dfrac{1}{9}=\dfrac{65}{9}-\dfrac{19}{9}=\dfrac{46}{9}\\ c,5-2\dfrac{4}{11}=5-\dfrac{26}{11}=\dfrac{29}{11}\\ d,5\dfrac{1}{2}-2\dfrac{1}{3}+2\dfrac{1}{6}=\dfrac{11}{2}-\dfrac{7}{3}+\dfrac{13}{6}=\dfrac{32}{6}=\dfrac{16}{3}\\ e,3\dfrac{4}{5}\times2\dfrac{1}{5}=\dfrac{19}{5}\times\dfrac{11}{5}=\dfrac{209}{25}\\ f,7\dfrac{2}{9}:2\dfrac{1}{9}=\dfrac{65}{9}:\dfrac{19}{9}=\dfrac{65}{9}\times\dfrac{9}{19}=\dfrac{65}{19}\\ g,5\times2\dfrac{4}{11}=5\times\dfrac{26}{11}=\dfrac{130}{11}\\ h,5:2\dfrac{4}{1}=5:8=\dfrac{5}{8}\)

bạn ơi câu h bị sao đúng ko?

tại tui thấy là 2 x 4 +1 = 9 

Gọi tổng trên là A.Ta có:

A=1/1x3+1/3x5+1/5x7+1/7x9+1/9x11

2A=2/1x3+2/3x5+2/5x7+2/7x9+2/9x11

2A=1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11

2A=1-1/11

2A=11/11-1/11

2A=10/11

  A=10/11:2

  A=5/11

a, = 1 - 1/2  + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/8 - 1/9

= 1 - 1/9

= 8/9

b và c biến tử = hiệu giữa 2 thừa số ở mẫu rồi làm như a

\(B=\frac{1}{1.2.3.4}+\frac{1}{2.3.4.5}+\frac{1}{3.4.5.6}+...+\frac{1}{8.9.10.11}+\frac{1}{9.10.11.12}\)

\(B=\frac{1}{3}\left(\frac{3}{1.2.3.4}+\frac{3}{2.3.4.5}+\frac{3}{3.4.5.6}+...+\frac{3}{8.9.10.11}+\frac{3}{9.10.11.12}\right)\)

\(B=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{2.3.4}+\frac{1}{2.3.4}-\frac{1}{3.4.5}+...+\frac{1}{9.10.11}-\frac{1}{10.11.12}\right)\)

\(B=\frac{1}{3}\left(\frac{1}{1.2.3}-\frac{1}{10.11.12}\right)\)

\(B=\frac{1}{3}.\frac{73}{440}=\frac{43}{1320}\)

98/99

KHÔNG CÓ CÁCH À

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, \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)

\(=1-\frac{1}{9}\)

\(=\frac{8}{9}\)