Rút gọn: A= \(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}......\frac{899}{900}\)
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25 tháng 5 2016
A=3/4x8/9x15/16x24/25x...x899/900
A=1.3/22 x 2.4/33 x 3.5/42 x 4.6/55 x ... x 29.31/302
A=1.2.3.4...29/2.3.4.5...30 x 3.4.5.6...31/2.3.4.5...30
A=1/30 x 31/2
A=31/60
B
23 tháng 2 2017
Ta có: A=\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}....\frac{899}{900}\)
\(\Leftrightarrow A=\frac{1.3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}.\frac{4.6}{5^2}....\frac{29.31}{30^2}\)
\(\Leftrightarrow A=\frac{1.2.3.4...29}{2.3.4.5...30}.\frac{3.4.5.6...31}{2.3.4.5...30}\)
\(\Leftrightarrow A=\frac{1}{30}.\frac{31}{2}\)
\(\Leftrightarrow A=\frac{1.31}{30.2}\)
\(\Leftrightarrow A=\frac{31}{60}\)
18 tháng 2 2017
\(A=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times...\times\frac{899}{900}\)
\(=\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times\frac{3.5}{4.4}\times...\times\frac{29.31}{30.30}\)
\(=\frac{\left(1\times2\times3\times...\times29\right)\left(3\times4\times5\times...\times31\right)}{\left(2\times3\times4\times...\times30\right)\left(2\times3\times4\times...\times30\right)}\)
\(=\frac{1\times2\times3\times...\times29}{2\times3\times4\times...\times30}.\frac{3\times4\times5\times...\times31}{2\times3\times4\times...\times30}\)
\(=\frac{1}{30}.\frac{31}{2}\)
\(=\frac{31}{60}\)
NT
19 tháng 2 2017
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{899}{900}\\ =\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}....\frac{29.31}{30.30}\\ =\frac{1.2.3.4....29}{2.3.4...30}.\frac{3.4.5...31}{2.3.4...30}\\ =\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)
.
23 tháng 2 2017
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}....\frac{899}{900}\)
\(A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.\frac{4.6}{5.5}....\frac{29.31}{30.30}\)
\(A=\frac{1.2.3.4....29}{2.3.4....30}.\frac{3.4.5.6...31}{2.3.4...30}\)
\(A=\frac{1}{30}.\frac{31}{2}\) (Rút gọn theo chiều /// và \\\ nhé)
\(A=\frac{31}{60}\)
Chúc học tốt!~~
26 tháng 2 2017
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}......\frac{889}{900}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}.....\frac{29\cdot31}{30.30}\)
\(=\frac{1.3.2.4.3.5.....29.31}{2.2.3.3.4.4....30.30}\)
\(=\frac{\left(1.2.3....29\right)\left(3.4.5...31\right)}{\left(2.3.4....30\right)\left(2.3.4.....30\right)}\)
\(=\frac{1.31}{30.2}=\frac{31}{60}\)
6 tháng 5 2016
A=\(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.........\frac{899}{900}\)
A=\(\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}..........\frac{29.31}{30.30}\)
A=\(\frac{1.2.3.......29}{2.3.4.......30}.\frac{3.4.5........31}{2.3.4.......30}\)
A=\(\frac{1}{30}.\frac{2}{31}=\frac{1}{465}\)
PT
4
CX
3 tháng 5 2016
A=3/4.8/9 .15/16.....899/900
A=1.3/2^2 . 2.4 /3^2 . 3.5/4^2 ....... 29.31 / 30^2
A= 1.2.3.....29 / 2.3.4....30 . 3.4.5...31 / 2.3.4....30
A=1/30 . 31/2
A= 31/60
Nhớ k nha
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{899}{900}\)
\(=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}....\frac{29.31}{30.30}\)
\(=\frac{1.2.3....29}{2.3.4....30}.\frac{3.4.5....31}{2.3.4....30}\)
\(=\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)
\(A=\frac{1\cdot3}{2\cdot2}\cdot\frac{2\cdot4}{3\cdot3}\cdot...\cdot\frac{29\cdot31}{30\cdot30}\)
\(A=\frac{1\cdot2\cdot...\cdot29}{2\cdot3\cdot...\cdot30}\cdot\frac{3\cdot4\cdot...\cdot31}{2\cdot3\cdot...\cdot30}=\frac{1}{30}\cdot\frac{31}{2}=\frac{31}{60}\)