\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}...\frac{399}{400}\Rightarrow A=\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}...\frac{19.21}{20.20}\Rightarrow\frac{1.2.3...19}{2.3.4...20}.\frac{3.4.5...21}{2.3.4...20}\) \(\Rightarrow A=\frac{1}{20}.\frac{21}{2}=\frac{21}{40}\)
Rút gọn : \(\left(1+\frac{1}{a+x}\right):\left(1-\frac{1}{a+x}\right).\left[1-\frac{1-\left(a^2+x^2\right)}{2ax}\right]\)
Cho \(A=\left(2-1\frac{1}{4}\right)\left(2-1\frac{1}{9}\right)\left(2-1\frac{1}{16}\right)...\left(2-1\frac{1}{400}\right)\)
Rút gọn A.
Rút gọn: \(\left(\frac{x^2}{4}+\frac{2}{x}\right):\left(\frac{x}{4}-\frac{1}{2}+\frac{1}{x}\right)\)
Rút gọn: \(\left(\frac{3a}{a^2-4}+\frac{1}{2-a}-\frac{2}{a+2}\right):\left(1-\frac{a^2+4}{a^2-4}\right)\)
Rút gọn : \(\left(x^2-\frac{1}{x}\right)\left(\frac{x+1}{x^2+x+1}+\frac{1}{x-1}\right)\)
Rút gọn : \(\frac{2}{xy}:\left(\frac{1}{x}-\frac{1}{y}\right)^2-\frac{x^2+y^2}{\left(x-y\right)^2}\)
Rút gọn: \(\left(\frac{3a+1}{a^2-3a}+\frac{3a-1}{a^2+3a}\right):\frac{a^2+1}{a^2-9}\)
Rút gọn : \(\left(\frac{1}{2x-y}+\frac{3y}{x^2-4x^2}-\frac{2}{2x+y}\right):\left(\frac{4x^2+y^2}{4x^2-y^2}+1\right)\)
Tính B = \(1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{16}\left(1+2+3+4+...+16\right)\)
