Tính: A= ( $\frac{1}{4}$-1) . ($\frac{1}{9}$-1) . … .($\frac{1}{2500}$-1) Làm nhanh mk tick cho 23/10/2021 Bởi Gianna Tính: A= ( $\frac{1}{4}$-1) . ($\frac{1}{9}$-1) . … .($\frac{1}{2500}$-1) Làm nhanh mk tick cho
Đáp án: $A=\dfrac{-51}{100}$ Giải thích các bước giải: $A=\left ( \dfrac{1}{4}-1 \right ).\left ( \dfrac{1}{9}-1 \right ).\left ( \dfrac{1}{16}-1 \right )…\left ( \dfrac{1}{2500}-1 \right )\\=\dfrac{-3}{4}.\dfrac{-8}{9}.\dfrac{-15}{16}…\dfrac{-2499}{2500}\\=\dfrac{-3}{2^2}.\dfrac{2.(-4)}{3^2}.\dfrac{3.(-5)}{4^2}…\dfrac{49.(-51)}{50^2}\\=\dfrac{1.2.3…49}{2.3.4…50}.\dfrac{(-3).(-4).(-5)…(-51)}{2.3.4…50}\\=\dfrac{1}{50}.\dfrac{-51}{2}\\=\dfrac{-51}{100}$ Bình luận
Đáp án:
$A=\dfrac{-51}{100}$
Giải thích các bước giải:
$A=\left ( \dfrac{1}{4}-1 \right ).\left ( \dfrac{1}{9}-1 \right ).\left ( \dfrac{1}{16}-1 \right )…\left ( \dfrac{1}{2500}-1 \right )\\
=\dfrac{-3}{4}.\dfrac{-8}{9}.\dfrac{-15}{16}…\dfrac{-2499}{2500}\\
=\dfrac{-3}{2^2}.\dfrac{2.(-4)}{3^2}.\dfrac{3.(-5)}{4^2}…\dfrac{49.(-51)}{50^2}\\
=\dfrac{1.2.3…49}{2.3.4…50}.\dfrac{(-3).(-4).(-5)…(-51)}{2.3.4…50}\\
=\dfrac{1}{50}.\dfrac{-51}{2}\\
=\dfrac{-51}{100}$