Question

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

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