\(\text{ P = (1 + \dfrac{7}{9}) (1 + \dfrac{7}{20}) (1 + \dfrac{7}{33})….(1 + \dfrac{7}{2900})}\)
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NV
Nguyễn Việt Lâm
Giáo viên
19 tháng 1
\(1+\dfrac{7}{n\left(n+8\right)}=\dfrac{n^2+8n+7}{n\left(n+8\right)}=\dfrac{\left(n+1\right)\left(n+7\right)}{n\left(n+8\right)}\)
\(\Rightarrow P=\left(1+\dfrac{7}{1.\left(1+8\right)}\right)\left(1+\dfrac{7}{2.\left(2+8\right)}\right)\left(1+\dfrac{7}{3.\left(3+8\right)}\right)...\left(1+\dfrac{7}{50.\left(50+8\right)}\right)\)
\(=\left(\dfrac{2.8}{1.9}\right).\left(\dfrac{3.9}{2.10}\right).\left(\dfrac{4.10}{3.11}\right)...\left(\dfrac{51.57}{50.58}\right)\)
\(=\dfrac{2.3.4...51}{1.2.3...50}.\dfrac{8.9.10...57}{9.10.11...58}=\dfrac{51}{1}.\dfrac{8}{58}=\dfrac{204}{29}\)
DH
17 tháng 8 2017
Đặt \(A=\left(1+\dfrac{7}{9}\right)\left(1+\dfrac{7}{20}\right)\left(1+\dfrac{7}{33}\right)....\left(1+\dfrac{7}{2900}\right)\)
\(B=\left(81-\dfrac{3}{4}\right)\left(81-\dfrac{3^2}{5}\right)\left(81-\dfrac{3^3}{6}\right)....\left(81-\dfrac{3^{2014}}{2017}\right)\)
Ta có:
\(A=\left(1+\dfrac{7}{9}\right)\left(1+\dfrac{7}{20}\right)\left(1+\dfrac{7}{33}\right).....\left(1+\dfrac{7}{2900}\right)\)
\(A=\dfrac{16}{9}.\dfrac{27}{20}.\dfrac{40}{33}.....\dfrac{2907}{2900}\)
\(A=\dfrac{2.8}{1.9}.\dfrac{3.9}{2.10}.\dfrac{4.10}{3.11}.....\dfrac{51.57}{50.58}\)
\(A=\dfrac{2.3.4.5.6....56.57}{1.2.3.4.5.....57.58}=\dfrac{1}{58}\)
\(B=\left(81-\dfrac{3}{4}\right)\left(81-\dfrac{3^2}{5}\right).....\left(81-\dfrac{3^{2014}}{2017}\right)\)
Vì trong dãy số trên có một thừa số là \(\left(81-\dfrac{3^6}{9}\right)=\left(81-81\right)=0\)
\(\Rightarrow B=0\)
Vì \(a=A+B\Rightarrow a=\dfrac{1}{58}+0=\dfrac{1}{58}\)(1)
Thay (1) vào đa thức \(f\left(x\right)=5x-29a\) ta được:
\(f\left(x\right)=5x-29.\dfrac{1}{58}=5x-\dfrac{1}{2}\)
Ta lại có:
\(f\left(x\right)=0\Leftrightarrow5x-\dfrac{1}{2}=0\Leftrightarrow x=\dfrac{1}{10}\)
Vậy nghiệm của đa thức trên là \(\dfrac{1}{10}\)
Chúc bạn học tốt!!!
24 tháng 6 2021
`a)1/7xx2/7+1/7xx5/7+6/7`
`=1/7xx(2/7+5/7)+6/7`
`=1/7xx1+6/7`
`=1/7+6/7=1`
`b)6/11xx4/9+6/11xx7/9-6/11xx2/9`
`=6/11xx(4/9+7/9-2/9)`
`=6/11xx9/9`
`=6/11`
24 tháng 6 2021
Sorry nãy ghi thiếu.
`c)4/25xx5/8xx25/4xx24`
`=(4xx5xx25xx24)/(25xx8xx4)`
`=(4xx5xx24)/(4xx8)`
`=(5xx24)/8`
`=5xx3=15`
O
3 tháng 5 2022
\(\dfrac{9}{5}+\dfrac{5}{7}+\dfrac{7}{5}+\dfrac{3}{7}=\left(\dfrac{9}{5}+\dfrac{7}{5}\right)+\left(\dfrac{5}{7}+\dfrac{3}{7}\right)=\dfrac{16}{5}+\dfrac{8}{7}=\dfrac{112}{35}+\dfrac{40}{35}=\dfrac{152}{35}\)
\(\dfrac{1}{2}\times\dfrac{45}{33}\times\dfrac{1}{9}\times\dfrac{11}{6}=\dfrac{1}{2}\times\dfrac{15}{11}\times\dfrac{1}{9}\times\dfrac{11}{6}=\left(\dfrac{1}{2}\times\dfrac{1}{9}\right)\times\left(\dfrac{15}{11}\times\dfrac{11}{6}\right)=\dfrac{1}{18}\times\dfrac{15}{6}=\dfrac{5}{36}\)
18 tháng 5 2017
\(\left(1+\dfrac{7}{9}\right)\left(1+\dfrac{7}{20}\right)\cdot\cdot\cdot\left(1+\dfrac{7}{180}\right)=\dfrac{16}{9}\cdot\dfrac{27}{20}\cdot\cdot\cdot\dfrac{187}{180}=\dfrac{2.8}{1\cdot9}\cdot\dfrac{3\cdot9}{2\cdot10}\cdot\cdot\cdot\dfrac{11\cdot17}{10\cdot18}=\dfrac{\left(2\cdot3\cdot...\cdot11\right)\cdot\left(8\cdot9\cdot...\cdot17\right)}{\left(1\cdot2\cdot...\cdot10\right)\cdot\left(9\cdot10\cdot...\cdot18\right)}=\dfrac{11\cdot8}{1\cdot18}=\dfrac{88}{18}=\dfrac{44}{9}\)
8 tháng 2 2022
\(\Leftrightarrow\left(11+\dfrac{7}{18}-9-\dfrac{13}{18}\right):x=\dfrac{5}{3}+\dfrac{35}{33}\cdot\dfrac{11}{7}=\dfrac{10}{3}\)
\(\Leftrightarrow x=\dfrac{5}{3}:\dfrac{10}{3}=\dfrac{1}{2}\)
1 tháng 7 2021
\(a,5x\dfrac{7}{3}=\dfrac{5}{1}x\dfrac{7}{3}=\dfrac{35}{3};b,\dfrac{13}{4}:7=\dfrac{13}{4} :\dfrac{7}{1}=\dfrac{13}{4}x\dfrac{1}{7}=\dfrac{13}{28}\)
H
1 tháng 7 2021
1. Tính
\(a,5\times\dfrac{7}{3}=\dfrac{35}{3}\)
\(b,\dfrac{13}{4}:7=\dfrac{13}{4}\times\dfrac{1}{7}=\dfrac{13}{28}\)
2. Tính
\(a,\dfrac{3}{7}+\dfrac{2}{5}+\dfrac{3}{4}\)
\(=\dfrac{15}{35}+\dfrac{14}{35}+\dfrac{3}{4}\)
\(=\dfrac{29}{35}+\dfrac{3}{4}\)
\(=\dfrac{116}{140}+\dfrac{105}{140}\)
\(=\dfrac{221}{140}\)
\(b,\dfrac{9}{7}-\dfrac{5}{11}\times\dfrac{11}{7}\)
\(=\dfrac{9}{7}-\dfrac{55}{77}\)
\(=\dfrac{99}{77}-\dfrac{55}{77}\)
\(=\dfrac{44}{77}=\dfrac{4}{7}\)
\(c,\dfrac{3}{5}\times\dfrac{5}{7}+\dfrac{4}{7}\)
\(=\dfrac{3}{5}\times\left(\dfrac{5}{7}+\dfrac{4}{7}\right)\)
\(=\dfrac{3}{5}\times\dfrac{9}{7}\)
\(=\dfrac{27}{35}\)
\(d,\dfrac{7}{9}\times\dfrac{2}{5}:\dfrac{3}{11}\)
\(=\dfrac{14}{45}:\dfrac{3}{11}\)
\(=\dfrac{14}{45}\times\dfrac{11}{3}\)
\(=\dfrac{154}{135}\)
\(e,\dfrac{9}{7}+\dfrac{2}{3}-\dfrac{1}{4}\)
\(=\dfrac{27}{21}+\dfrac{14}{21}-\dfrac{1}{4}\)
\(=\dfrac{41}{21}-\dfrac{1}{4}\)
\(=\dfrac{164}{84}-\dfrac{21}{84}\)
\(=\dfrac{143}{84}\)
\(g,\dfrac{4}{9}:\dfrac{3}{5}\times\dfrac{2}{11}\)
\(=\dfrac{4}{9}\times\dfrac{5}{3}\times\dfrac{2}{11}\)
\(=\dfrac{20}{27}\times\dfrac{2}{11}\)
\(=\dfrac{40}{297}\)
\(h,\dfrac{7}{2}-\dfrac{3}{10}:\dfrac{2}{5}\)
\(=\left(\dfrac{7}{2}-\dfrac{3}{10}\right):\dfrac{2}{5}\)
\(=\left(\dfrac{35}{10}-\dfrac{3}{10}\right):\dfrac{2}{5}\)
\(=\dfrac{32}{10}:\dfrac{2}{5}\)
\(=\dfrac{16}{5}\times\dfrac{5}{2}\)
\(=\dfrac{80}{10}=8\)
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