Cm A=1/1.3 +1/3.5 +…+1/(2n-1)(2n+1) <1/2

2 bình luận về “Cm A=1/1.3 +1/3.5 +…+1/(2n-1)(2n+1) <1/2”

1. A=1/(1*3)+1/(3*5)+…+1/((2n-1)*(2n+1))

   =1/2*(2/(1*3)+2/(3*5)+…+2/((2n-1)*(2n+1)))

   =1/2*(1-1/3+1/3-1/5+…+1/(2n-1)-1/(2n+1))

   =1/2*(1-1/(2n+1))

   =1/2-1/(2n+1)

   =>A<1/2

   Trả lời
2. A=(1)/(1.3) + (1)/(3.5) + … + (1)/((2n-1).(2n+1))

   => 2A = (2)/(1.3) + (2)/(3.5) + … (2)/((2n-1).(2n+1))

   => 2A = 1 – 1/3 + 1/3 – 1/5 + 1/5 – … + (1)/(2n-1) – (1)/(2n+1)

   => A= 1/2 . (1 – (1)/(2n+1))

   => A= 1/2 – (1)/(2n +1) < 1/2

   => A < 1/2.

    

   Trả lời