Cho P=(1-1/2 ²).(1-1/3 ²).(1-1/4 ²)….(1-1/50 ²). So sánh P với 1/2 11/10/2021 Bởi Audrey Cho P=(1-1/2 ²).(1-1/3 ²).(1-1/4 ²)….(1-1/50 ²). So sánh P với 1/2
Đáp án: $P>\dfrac{1}{2}$ Giải thích các bước giải: $P=\left ( 1-\dfrac{1}{2^2} \right ).\left ( 1-\dfrac{1}{3^2} \right ).\left ( 1-\dfrac{1}{4^2} \right )…\left ( 1-\dfrac{1}{50^2} \right )\\=\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}…\dfrac{2499}{50^2}\\=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}…\dfrac{49.51}{50.50}\\=\dfrac{1.2.3.4…49}{2.3.4…50}.\dfrac{3.4.5…51}{2.3.4…50}\\=\dfrac{1}{50}.\dfrac{51}{2}\\=\dfrac{51}{100}>\dfrac{1}{2}$ Bình luận
Đáp án:
$P>\dfrac{1}{2}$
Giải thích các bước giải:
$P=\left ( 1-\dfrac{1}{2^2} \right ).\left ( 1-\dfrac{1}{3^2} \right ).\left ( 1-\dfrac{1}{4^2} \right )…\left ( 1-\dfrac{1}{50^2} \right )\\
=\dfrac{3}{2^2}.\dfrac{8}{3^2}.\dfrac{15}{4^2}…\dfrac{2499}{50^2}\\
=\dfrac{1.3}{2.2}.\dfrac{2.4}{3.3}.\dfrac{3.5}{4.4}…\dfrac{49.51}{50.50}\\
=\dfrac{1.2.3.4…49}{2.3.4…50}.\dfrac{3.4.5…51}{2.3.4…50}\\
=\dfrac{1}{50}.\dfrac{51}{2}\\
=\dfrac{51}{100}
>\dfrac{1}{2}$