Question

bài 1 : tính

1) A = \(\left(\frac{1}{2}+1\right).\left(\frac{1}{3}+1\right).\left(\frac{1}{4}+1\right)........\left(\frac{1}{99}+1\right)\) 

2) B = \(\left(\frac{1}{2}-1\right).\left(\frac{1}{3}-1\right).\left(\frac{1}{4}-1\right).....\left(\frac{1}{99}-1\right)\)

 

Answer 1

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

   A= \(\frac{100}{2}\)

   A=50

2, B=\(\frac{-1}{2}.\frac{-2}{3}....\frac{-98}{99}\)

     B= \(\frac{1}{99}\)

Answer 2

\(A=\left(\frac{1}{2}+1\right)\cdot\left(\frac{1}{3}+1\right)\cdot\left(\frac{1}{4}+1\right)......\left(\frac{1}{99}+1\right)\)

     \(=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}......\frac{99}{98}\cdot\frac{100}{99}\)

     \(=\frac{100}{2}\)

       \(=50\)

\(B=\left(\frac{1}{2}-1\right)\cdot\left(\frac{1}{3}-1\right)\cdot\left(\frac{1}{4}-1\right)......\left(\frac{1}{99}-1\right)\)

     \(=\left(-\frac{1}{2}\right)\cdot\left(-\frac{2}{3}\right)\cdot\left(-\frac{3}{4}\right).....\left(-\frac{97}{98}\right)\cdot\left(-\frac{98}{99}\right)\)

       \(=-\frac{1}{99}\)