Bài 1: Tính
a)\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right).....\left(1-\frac{1}{n+1}\right)\)
b)\(\frac{1}{2000.1999}-\frac{1}{1999-1998}-\frac{1}{1998-1997}-...-\frac{1}{3.2}-\frac{1}{2.1}\)
c)\(-3+\frac{1}{1+\frac{1}{3+\frac{1}{1+\frac{1}{3}}}}\)
câu b sai đề bạn ơi
a)
\(\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)...\left(1-\frac{1}{n+1}\right)\)
\(=\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{n}{n+1}\)
\(=\frac{1\cdot2\cdot3\cdot...\cdot n}{2\cdot3\cdot4\cdot...\cdot\left(n+1\right)}\)
\(=\frac{1}{n+1}\)