\(A=3\cdot\frac{1}{1\cdot2}-5\cdot\frac{1}{2\cdot3}+7\cdot\frac{1}{3\cdot4}-\cdots+15\cdot\frac{1}{7\cdot8}-17\cdot\frac{1}{8\cdot9}\)

\(=\frac{3}{1\cdot2}-\frac{5}{2\cdot3}+\frac{7}{3\cdot4}-\cdots+\frac{15}{7\cdot8}-\frac{17}{8\cdot9}\)

\(=1+\frac12-\frac12-\frac13+\frac13+\frac14-\cdots+\frac17+\frac18-\frac18-\frac19\)

\(=1-\frac19=\frac89\)

\(\) Ta có:

\(A=\frac{3\cdot1}{1\cdot2}-\frac{5\cdot1}{2\cdot3}+\frac{7\cdot1}{3\cdot4}-\cdots+\frac{15\cdot1}{7\cdot8}-\frac{17\cdot1}{8\cdot9}\)

\(A=\frac{3}{1\cdot2}-\frac{5}{2\cdot3}+\frac{7}{3\cdot4}-\cdots+\frac{15}{7\cdot8}-\frac{17}{8\cdot9}\)

\(A=\frac{1+2}{1\cdot2}-\frac{2+3}{2\cdot3}+\frac{3+4}{3\cdot4}-\cdots+\frac{7+8}{7\cdot8}-\frac{8+9}{8\cdot9}\)

\(A=\left(\frac11+\frac12\right)-\left(\frac12+\frac13\right)+\left(\frac13+\frac14\right)-\cdots+\left(\frac17+\frac18\right)-\left(\frac18+\frac19\right)\)

\(A=\frac11+\frac12-\frac12-\frac13+\frac13+\frac14-\cdots+\frac17+\frac18-\frac18-\frac19\)

\(A=1-\frac19\)

\(A=\frac89\)

Vậy \(A=\frac89\)

\(A=3\cdot\frac{1}{1\cdot2}-5\cdot\frac{1}{2\cdot3}+7\cdot\frac{1}{3\cdot4}-\cdots+15\cdot\frac{1}{7\cdot8}-17\cdot\frac{1}{8\cdot9}\)

\(=\frac{3}{1\cdot2}-\frac{5}{2\cdot3}+\frac{7}{3\cdot4}-\cdots+\frac{15}{7\cdot8}-\frac{17}{8\cdot9}\)

\(=1+\frac12-\frac12-\frac13+\frac13+\frac14-\cdots+\frac17+\frac18-\frac18-\frac19\)

\(=1-\frac19=\frac89\)

áp dụng công thức này là làm được bạn ạ:

\(\frac{a}{b.c}\) =\(\frac{a}{b}-\frac{a}{c}\)

TA có: \(\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\cdots+\frac{1}{8\cdot9}\right)\cdot100-\left\lbrack\frac52-\left(x+\frac{206}{100}\right)\right\rbrack:\frac12=\frac89\)

=>\(\left(1-\frac12+\frac12-\frac13+\cdots+\frac18-\frac19\right)\cdot100-\left\lbrack\frac52-\left(x+\frac{13}{50}\right)\right\rbrack\cdot2=\frac89\)

=>\(\frac89\cdot100-\left\lbrack\frac52-\left(x+\frac{13}{50}\right)\right\rbrack\cdot2=\frac89\)

=>\(2\cdot\left\lbrack\frac52-\left(x+\frac{13}{50}\right)\right\rbrack=\frac89\cdot99=88\)

=>\(\frac52-\left(x+\frac{13}{50}\right)=44\)

=>\(x+\frac{13}{50}=\frac52-44=2,5-44=-41,5\)

=>x+0,26=-41,5

=>x=-41,5-0,26

=>x=-41,76

Tích bằng:

8x9=72

Đáp số: 72

8 x 9 = 72

\(8.9+8.1+.11\)

\(=8.\left(9+1\right).11\)

\(=8.10.11\)

\(=80.11\)

\(=880\)

=72+8x11

=72+88

=160

1 + 8x9 = 1 +72

             = 73

1+8*9

=1+72(nhân chia trước cộng trừ sau)

=73

bằng 95