Toán Cho P=(1-1/2^2).(1-1/3^2).(1-1/4^2)…(1-1/50^2). So sánh P với 1/2 10/10/2021 By Bella Cho P=(1-1/2^2).(1-1/3^2).(1-1/4^2)…(1-1/50^2). So sánh P với 1/2
=(2^2-1/2^2).(3^2-1/3^2)…..(50^2-1/50^2) =(1.3/2^2).(2.4/3^2)……(49.51/50^2) =(1.2.3.4…..49).(3.4.5…51)/(2.3.4…..50).(2.3.4…..50) =51/2.50=51/100 Trả lời
$P = \dfrac{1-1}{2^2} . \dfrac{1-1}{3^2} . \dfrac{1-1}{4^2} . … . \dfrac{1-1}{50^2}$ $P = \dfrac{0}{2^2} . \dfrac{0}{3^2} . … . \dfrac{0}{50^2}$ $P = 0 . 0 . 0 . … . 0$ $P = 0$ $-> P < \dfrac{1}{2}$ Trả lời
=(2^2-1/2^2).(3^2-1/3^2)…..(50^2-1/50^2)
=(1.3/2^2).(2.4/3^2)……(49.51/50^2)
=(1.2.3.4…..49).(3.4.5…51)/(2.3.4…..50).(2.3.4…..50)
=51/2.50=51/100
$P = \dfrac{1-1}{2^2} . \dfrac{1-1}{3^2} . \dfrac{1-1}{4^2} . … . \dfrac{1-1}{50^2}$
$P = \dfrac{0}{2^2} . \dfrac{0}{3^2} . … . \dfrac{0}{50^2}$
$P = 0 . 0 . 0 . … . 0$
$P = 0$
$-> P < \dfrac{1}{2}$