Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(1\frac{1}{7}\cdot1\frac{1}{8}\cdot1\frac{1}{9}\cdot...\cdot1\frac{1}{50}\)
\(=\frac{8}{7}\cdot\frac{9}{8}\cdot\frac{10}{9}\cdot...\cdot\frac{51}{50}\)
\(=\frac{8\cdot9\cdot10\cdot...\cdot51}{7\cdot8\cdot9\cdot...\cdot50}\)
\(=\frac{51}{7}\)
\(\left(1-\frac{1}{9}\right)x\left(1-\frac{1}{16}\right)x\left(1-\frac{1}{21}\right)x.........x\left(1-\frac{1}{210}\right)\)
= \(\frac{8}{9}x\frac{15}{16}x\frac{20}{21}x.........x\frac{209}{210}\)
Sau đó bạn tìm ra quy luật thôi
Tính nhanh:
3/4 : 0,75 + 50% : 1/2 + 4/5 x 1 1/4
= 0,75 : 0,75 + 1/2 : 1/2 + 4/5 x 5/4
= 1 + 1 + 1
= 3
\(=\frac{3}{4}:\frac{3}{4}+\frac{1}{2}:\frac{1}{2}+\frac{4}{5}.\frac{5}{4}\)
\(=1+1+1\)
\(=3\)
Chúc bạn học tốt
1) a) \(\frac{5454}{5757}-\frac{171717}{191919}=\frac{18\times3\times101}{19\times3\times101}-\frac{17\times10101}{19\times10101}=\frac{18}{19}-\frac{17}{19}=\frac{1}{19}\)
b) \(\frac{6}{5}\times\frac{7}{6}\times\frac{8}{7}\times....\times\frac{2021}{2020}=\frac{6\times7\times8\times...\times2021}{5\times6\times7\times...\times2020}=\frac{2021}{5}\)
2) \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{45}=2\times\frac{1}{6}+2\times\frac{1}{12}+2\times\frac{1}{20}+...+2\times\frac{1}{90}\)
\(=2\times\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}\right)\)
\(=2\times\left(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+...+\frac{1}{9\times10}\right)\)
\(=2\times\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)=2\times\left(\frac{1}{2}-\frac{1}{10}\right)=2\times\frac{2}{5}=\frac{4}{5}\)
b)Vì \(a-1< a+1\)
=> \(\frac{1}{a-1}>\frac{1}{a+1}\)
Câu 1: \(\frac{5}{7}\):x+\(\frac{2}{3}\)=1\(\frac{1}{3}\)
\(\frac{5}{7}\):x+\(\frac{2}{3}\)=\(\frac{4}{3}\)
\(\frac{5}{7}\):x=\(\frac{4}{3}\) - \(\frac{2}{3}\)
\(\frac{5}{7}\):x=\(\frac{2}{3}\)
x=\(\frac{5}{7}\):\(\frac{2}{3}\)
x=\(\frac{15}{14}\)
Câu 2:x*\(\frac{3}{7}\)-\(\frac{5}{14}\)=2\(\frac{1}{3}\)
x*\(\frac{3}{7}\)-\(\frac{5}{14}\)=\(\frac{7}{3}\)
x*\(\frac{3}{7}\)=\(\frac{7}{3}\)+\(\frac{5}{14}\)
x*\(\frac{3}{7}\)=\(\frac{113}{42}\)
x=\(\frac{113}{42}\):\(\frac{3}{7}\)
x=\(\frac{791}{126}\)
Câu 3: 3\(\frac{5}{7}\)-x*\(\frac{1}{3}\)=1\(\frac{13}{11}\)
\(\frac{26}{7}\)-x*\(\frac{1}{3}\)=\(\frac{24}{11}\)
x*\(\frac{1}{3}\)=\(\frac{26}{7}\)-\(\frac{24}{11}\)
x*\(\frac{1}{3}\)=\(\frac{118}{77}\)
x=\(\frac{118}{77}\):\(\frac{1}{3}\)
x=\(\frac{356}{77}\)
#)Giải :
Đặt \(A=\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+\frac{1}{9.10}\)
\(A=\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\)
\(A=\frac{1}{5}-\frac{1}{10}\)
\(A=\frac{1}{10}\)
\(\left(1\frac{1}{7}\right)\left(1\frac{1}{8}\right)\left(1\frac{1}{9}\right)...\left(1\frac{1}{50}\right)\)
\(=\frac{8}{7}.\frac{9}{8}.\frac{10}{9}...\frac{51}{50}\)
\(=\frac{8.9.10...51}{7.8.9...50}\)
\(=\frac{51}{7}\)
\(=\frac{8}{7}\times\frac{9}{8}\times\frac{10}{9}\times...\times\frac{51}{50}\)
\(=\frac{51}{7}\)