Ta có: \(A=\frac{5^2}{1\cdot6}+\frac{5^2}{6\cdot11}+...+\frac{5^2}{26\cdot31}\)
\(=5\left(\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+...+\frac{5}{26\cdot31}\right)\)
\(=5\cdot\left(1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{26}-\frac{1}{31}\right)\)
\(=5\cdot\left(1-\frac{1}{31}\right)=5\cdot\frac{30}{31}=\frac{150}{31}>1\)
hay A>1(đpcm)
A=\(\frac{\frac{1}{3}-\frac{5}{2}}{\frac{3}{4}-\frac{1}{2}}\).\(\frac{\frac{5}{6}+\frac{7}{3}}{1-\frac{5}{6}}\).\(\frac{-\frac{2}{5}+1}{\frac{2}{5}+1}\)
B=\(\frac{\frac{1}{3}-\frac{4}{5}}{\frac{1}{3}-\frac{4}{5}}\).\(\frac{\frac{3}{4}-\frac{5}{3}}{\frac{3}{4}+\frac{5}{3}}\):\(\frac{\frac{4}{5}-1}{1-\frac{2}{3}}\)
mong mọi người giải giúp em
1) chứng minh : \(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{49.50}=\frac{1}{26}+\frac{1}{27}+...+\frac{1}{50}\)
2) cho :\(A=\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{99.100}\)Chứng minh \(\frac{7}{12}< A< \frac{5}{6}\)
Tính = cák hợp lý:
a) \(139\frac{5}{7}:\frac{2}{3}-138\frac{2}{7}:\sqrt{\frac{4}{9}}\)
b) \(\left(\frac{-5}{11}:\frac{13}{18}-\frac{5}{11}:\frac{13}{5}\right)+\frac{-1}{33}\)
c) \(\left|97\frac{2}{3}-125\frac{3}{5}\right|+97\frac{2}{5}-125\frac{1}{3}\)
a)\(\frac{-3}{2}-2x+\frac{3}{4}=-2\)
b)\(\left(\frac{-2}{3}x-\frac{3}{5}\right)\left(\frac{3}{-2}-\frac{10}{3}\right)=\frac{2}{5}\)
c)\(\frac{x}{2}-\left(\frac{3x}{5}-\frac{13}{5}\right)=-\left(\frac{7}{5}+\frac{7}{10}.x\right)\)
d)\(\frac{2x-3}{3}+\frac{-3}{2}=\frac{5-3x}{6}-\frac{1}{3}\)
e)\(\frac{2}{3x}-\frac{3}{12}=\frac{4}{5}-\left(\frac{7}{x}2\right)\)
k)\(\frac{13}{x-1}+\frac{5}{2x-2}-\frac{6}{3x-3}\)
m)\(\left(\frac{3}{2}-\frac{2}{-5}\right):x-\frac{1}{2}=\frac{3}{2}\)
n)\(\left(\frac{3}{2}-\frac{5}{11}-\frac{3}{13}\right)\left(2x-2\right)=\left(\frac{-3}{4}+\frac{5}{22}+\frac{3}{26}\right)\)
Giải giúp mk
mk đang cần ghấp trong hôm nay
cám ơn mọi người
a, \(5\frac{4}{13}.15\frac{3}{41}-5\frac{4}{13}.2\frac{3}{41}\)
b, \(6.(-\frac{1}{3})^2-(\frac{1}{4}:2-\frac{7}{16}.\frac{-4}{21})\)
Tìm x, biết:
a) \(\left(\frac{4}{13}.\frac{6}{5}+\frac{4}{13}.\frac{2}{5}\right).\left(2x+1\right)^2=\frac{10}{13}\)
b) \(\frac{x-1}{x+5}=\frac{6}{7}\)
Tính:
a. \(5\frac{4}{23}.27\frac{3}{47}+4\frac{3}{47}\left(-5\frac{4}{23}\right)\)
b. \(A=1+2+5...+\frac{3^{\text{n}-1}+1}{2}\) (n \(\in\) N)
Tìm x
a, \(\frac{1}{3}x-\frac{2}{5}.\left(x+1\right)=0\)
b, \(\frac{x+2}{0,5}=\frac{2x+1}{2}\)
c, \(|x+\frac{1}{5}|-4=2\)
d, \(\left(\frac{1}{4}x-1,5\right)+\left(\frac{5}{6}x-3\right)-\left(\frac{5}{8}x-0,5\right)=-4,5\)
Tính
a, \(\frac{2^5.8^4.4^3}{16^6}\)
b, \(\frac{\left(\frac{1}{6}\right)^2.6^2+\left(0,6\right)^5}{\left(0,2\right)^5}\)
c, \(\left(\frac{3}{5}-\frac{3}{4}\right).\left(\frac{2}{6}-\frac{1}{5}\right)^2\)
d, \(\frac{8^4.3^6}{2^7.65}\)
e, \(\frac{2^5.49^2}{4^3.7^3}\)
