Question

Tính bằng cách hợp lí :

\(B=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.......\frac{99}{100}\)

Answer 1

B = 1.3/2.2 . 2.4/3.3 . 3.5/4.4 . ...... . 9.11/10.10

   = 1.2.3 . ..... . 9/2.3.4 . ..... . 10   .   3.4.5 . ...... . 11/2.3.4 . ..... . 10

   = 1/10 . 11/2

   = 11/20

Tk mk nha

Answer 2

\(B=\frac{3}{4}.\frac{8}{9}...\frac{99}{100}\)

\(B=\frac{1\cdot3}{2^2}.\frac{2\cdot4}{3^3}...\frac{9\cdot11}{10^2}\)

\(B=\frac{1.3.2.4...9.11}{2^2.3^3...10^2}\)

\(B=\frac{11}{2.10}\)

\(B=\frac{11}{20}\)