Question

1.Tính nhanh:

a,(1-1/2)x(1-1/3)x(1-1/4)x....x(1-1/100)

b,(1-1/25)x(1-2/7)x(1-2/9)x.....x(1-2/99)

c,1987x1986-1/1985x1987x1986

Answer 1

a, = 1/2 x 2/3 x 3/4 x .... x 99/100 = 1/100

b, = 24/25 x 5/7 x 7/9 x .... x 97/99 = 24/25 x 5/99 = 8/165

Answer 2

a) \(\left(1-\frac{1}{2}\right)\cdot\left(1-\frac{1}{3}\right)\cdot\left(1-\frac{1}{4}\right)\cdot...\cdot\left(1-\frac{1}{100}\right)\)

=\(\frac{1}{2}\cdot\frac{2}{3}\cdot\frac{3}{4}\cdot...\cdot\frac{99}{100}\)

=