Tính  \(\frac{1\cdot3\cdot5\cdot7\cdot9...99}{50\cdot51\cdot52...100}\)

Cho \(U_1=\frac{1}{1\cdot3\cdot5}\); \(U_2=\frac{1}{1\cdot3\cdot5}+\frac{1}{3\cdot5\cdot7}\); \(U_3=\frac{1}{1\cdot3\cdot5}+\frac{1}{3\cdot5\cdot7}+\frac{1}{5\cdot7\cdot9}\)

a) Lập quy trình tổng quát tính U_n

b) Tính U₅₀, U₆₀

c) Tính U₁₀₀₂

Giúp mk bài này nha.

Tính : \(B=1\cdot3^3+3\cdot5^3+5\cdot7^3+...+49\cdot51^3\)

 \(\frac{1}{50\cdot51}+\frac{1}{51\cdot52}+\frac{1}{52\cdot53}+...+\frac{1}{99\cdot100}\)tính kết quả

\(tinh;\frac{1}{51\cdot100}+\frac{1}{52\cdot99}+...+\frac{1}{99\cdot52}+\frac{1}{100\cdot51}\)

Tính \(E=1\cdot3^3+3\cdot5^3+5\cdot7^3+...+49\cdot51^3\) 

Tính \(F=1\cdot99^2+2\cdot98^2+3\cdot97^2+...+49\cdot51^2\)

Giúp ! Giúp ! Giúp, nhanh lên.

Tính nhanh :

\(A=\left(1-\frac{2}{6\cdot7}\right)\left(1-\frac{2}{7\cdot8}\right)\left(1-\frac{2}{8\cdot9}\right)\cdot\cdot\cdot\left(1-\frac{2}{51\cdot52}\right)\)

\(B=\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)\left(1+\frac{1}{3\cdot5}\right)\cdot\cdot\cdot\left(1+\frac{1}{99\cdot101}\right)\)

\(\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\frac{4^2}{3\cdot5}...\frac{50^2}{49\cdot51}=?\)

\(\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\frac{4^2}{3\cdot5}...\frac{50^2}{49\cdot51}=?\)