Toán chứng minh rằng : 1/2^2+1/3^2+1/4^2+…+1/100<1 12/09/2021 By Margaret chứng minh rằng : 1/2^2+1/3^2+1/4^2+…+1/100<1
`A =1/2^2 + 1/3^2 + 1/4^2 + … + 1/100^2` `⇒ A = 1/2.2 + 1/3.3 + 1/4.4 + … + 1/100.100` `⇒ A < 1/1.2 + 1/2.3 + 1/3.4 + … + 1/99.100` `⇒ 1/1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + … + 1/99 – 1/100` `⇒ A < 1 – 1/100` `⇒ A < 1` Trả lời
Đáp án:
Giải thích các bước xin ctlhn nha
`A =1/2^2 + 1/3^2 + 1/4^2 + … + 1/100^2`
`⇒ A = 1/2.2 + 1/3.3 + 1/4.4 + … + 1/100.100`
`⇒ A < 1/1.2 + 1/2.3 + 1/3.4 + … + 1/99.100`
`⇒ 1/1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + … + 1/99 – 1/100`
`⇒ A < 1 – 1/100`
`⇒ A < 1`