1) Hãy tính:

A= (1 + 2 +3 + ... + 100) - (\(\frac{1}{2}\)+ \(\frac{2}{3}\)+ \(\frac{3}{4}\)+ ... + \(\frac{49}{50}\))

B=( \(\frac{1}{2\frac{3}{4}}\)+  \(\frac{1}{3\frac{4}{5}}\)+  \(\frac{1}{4\frac{5}{6}}\)+ ... + \(\frac{1}{98\frac{99}{100}}\)) - ( \(\frac{1}{2}\). \(\frac{3}{4}\)\(\frac{5}{6}\)...  \(\frac{99}{100}\))

2) Tìm x để:

a) \(\left(x+10\right).\left(x+20\right)...\left(x+500\right)=5000000\)

b) \(\frac{1}{2}\)\(x\) + \(\frac{3}{4}\)\(x\) + ... + \(\frac{100}{101}\)\(x\) = \(5000\)

\(\frac{\sqrt{x-5}}{45}\). \(\frac{\frac{6}{7}}{\sqrt{4^{75}}+25}\) - \(\left(\frac{4}{5}+\frac{6}{7}+...+\frac{50}{51}\right)\) = \(300x\)

a)cho A = \(\frac{5}{4}\)+ \(\frac{5}{4^2}\)+ \(\frac{5}{4^3}\)+.......+ \(\frac{5}{4^{99}}\)  .CHỨNG MINH RẰNG A < \(\frac{5}{3}\)

b)cho E = \(\frac{1}{3}\)+ \(\frac{2}{3^2}\)+ \(\frac{3}{3^3}\)+.......+ \(\frac{100}{3^{100}}\).CHỨNG MINH RẰNG E < \(\frac{3}{4}\)

1) \(\frac{x}{5}\)=\(\frac{y}{4}\)và x\(^2\)y= 100

2) 5x = 2y và x\(^3\)y\(^2\) = 200

3) \(\frac{x}{3}\)=\(\frac{y}{4}\)và x\(^2\)+ y\(^2\)= 100

4)\(\frac{x}{4}\)=\(\frac{y}{7}\)và 3x\(^2\)- 4y\(^2\)=100

5)\(\frac{x}{5}\)=\(\frac{y}{2}\)=\(\frac{z}{-3}\)và x y z = 240

A= \(\frac{-2}{2\cdot3}\)+\(\frac{-2}{4\cdot5}\)+\(\frac{-2}{6\cdot7}\)+...+\(\frac{-2}{99\cdot100}\)

A= \(\frac{-1}{2}\)-\(\frac{-1}{3}\)+\(\frac{-1}{4}\)-\(\frac{-1}{5}\)+...+\(\frac{-1}{99}\)-\(\frac{-1}{100}\)