cho Q=(1-1/2²)×(1-1/3²)×(1-1/4²)ו••×(1-1/40²). So sánh Q với 1/2 giúp mình với,cảm ơn các bạn 18/08/2021 Bởi Isabelle cho Q=(1-1/2²)×(1-1/3²)×(1-1/4²)ו••×(1-1/40²). So sánh Q với 1/2 giúp mình với,cảm ơn các bạn
(1-1/2²)×(1-1/3²)×(1-1/4²)ו••×(1-1/40²) =3/4×8/9×15/16×..×1599/1600 =(1×3/2×2)×(2×4/3×3)×..×(39×41/40×40) =(1×2×3×4×..×39/2×3×4×5×..×40)×(3×4×5×6×..×41/2×3×4×5×..×40) =1/40×41/2 =41/80>40/80=1/2 Bình luận
Tham khảo `Q=(1-\frac{1}{2^2})(1-\frac{1}{3^2})(1-\frac{1}{4^2})…..(1-\frac{1}{40^2})` `⇒Q=\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}.\frac{4^2-1}{4^2}…..\frac{40^2-1}{40^2}` `⇒Q=\frac{3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}….\frac{39.40}{40^2}` `⇒Q=\frac{(2.3…..39).(3.4.5…..41)}{(2.3.4….40).(2.3.4….40)}` `⇒Q=\frac{1}{40}.\frac{41}{2}` `⇒Q=\frac{41}{80}>\frac{40}{80}=\frac{1}{2}` `\text{©CBT}` Bình luận
(1-1/2²)×(1-1/3²)×(1-1/4²)ו••×(1-1/40²)
=3/4×8/9×15/16×..×1599/1600
=(1×3/2×2)×(2×4/3×3)×..×(39×41/40×40)
=(1×2×3×4×..×39/2×3×4×5×..×40)×(3×4×5×6×..×41/2×3×4×5×..×40)
=1/40×41/2
=41/80>40/80=1/2
Tham khảo
`Q=(1-\frac{1}{2^2})(1-\frac{1}{3^2})(1-\frac{1}{4^2})…..(1-\frac{1}{40^2})`
`⇒Q=\frac{2^2-1}{2^2}.\frac{3^2-1}{3^2}.\frac{4^2-1}{4^2}…..\frac{40^2-1}{40^2}`
`⇒Q=\frac{3}{2^2}.\frac{2.4}{3^2}.\frac{3.5}{4^2}….\frac{39.40}{40^2}`
`⇒Q=\frac{(2.3…..39).(3.4.5…..41)}{(2.3.4….40).(2.3.4….40)}`
`⇒Q=\frac{1}{40}.\frac{41}{2}`
`⇒Q=\frac{41}{80}>\frac{40}{80}=\frac{1}{2}`
`\text{©CBT}`