Đáp án:
$A=\dfrac{-51}{100}$
Giải thích các bước giải:
$A=\left ( \dfrac{1}{4}-1 \right ).\left ( \dfrac{1}{9}-1 \right ).\left ( \dfrac{1}{16}-1 \right )...\left ( \dfrac{1}{2500}-1 \right )\\
=\dfrac{-3}{4}.\dfrac{-8}{9}.\dfrac{-15}{16}...\dfrac{-2499}{2500}\\
=\dfrac{-3}{2^2}.\dfrac{2.(-4)}{3^2}.\dfrac{3.(-5)}{4^2}...\dfrac{49.(-51)}{50^2}\\
=\dfrac{1.2.3...49}{2.3.4...50}.\dfrac{(-3).(-4).(-5)...(-51)}{2.3.4...50}\\
=\dfrac{1}{50}.\dfrac{-51}{2}\\
=\dfrac{-51}{100}$