Question

[ツ ✞ঔৣ۝ѕк ѕơиʚɞᴾᴿᴼシ ╾━╤デ╦︻]

1. Cho A = 1/2 . 3/4 . 5/6 .....99/100

Chứng minh A^2 < 1/101

Answer 1

[✪ ω ✪Mùa⚜ hoa⚜ phượng⚜ là⚜ mùa⚜ th...]

$A=\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}$

$\Rightarrow A<\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}$

$\Rightarrow A^2<\frac{2}{3}.\frac{4}{5}.\frac{6}{7}...\frac{100}{101}.\frac{1}{2}.\frac{3}{4}.\frac{5}{6}...\frac{99}{100}$

$\Rightarrow A^2<\frac{1}{101}<\frac{1}{100}=\frac{1}{{10}^2}$

$\iff A<$