Toán B=2×2012/(1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+2012)) tính giá trị B 01/07/2021 By Alaia B=2×2012/(1+1/(1+2)+1/(1+2+3)+…+1/(1+2+3+4+…+2012)) tính giá trị B
`B=2.2012/{1+1/{1+2}+1/{1+2+3}+…+1/{1+2+3+4+…+2012}}` Đặt `C=1+1/{1+2}+1/{1+2+3}+…+1/{1+2+3+4+…+2012}` Ta có công thức: `1+2+3+…+n={n.(n+1)}/2` Thay vào `C``⇒C=1+1/{{2.3}/2}+1/{{3.4}/2}+…+1/{{2012.2013}/2}` `⇒C/2=1/2+1/2.3+1/3.4+…+1/2012.2013` `⇒C/2=1/2+1/2-1/3+1/3-1/4+…+1/2012-1/2013` `⇒C/2=1-1/2013` `⇒C/2=2012/2013` `⇒C=4024/2013` `⇒B=4024/{4024/2013}` `⇒B=2013` Trả lời
`B=2.2012/{1+1/{1+2}+1/{1+2+3}+…+1/{1+2+3+4+…+2012}}`
Đặt `C=1+1/{1+2}+1/{1+2+3}+…+1/{1+2+3+4+…+2012}`
Ta có công thức: `1+2+3+…+n={n.(n+1)}/2`
Thay vào `C`
`⇒C=1+1/{{2.3}/2}+1/{{3.4}/2}+…+1/{{2012.2013}/2}`
`⇒C/2=1/2+1/2.3+1/3.4+…+1/2012.2013`
`⇒C/2=1/2+1/2-1/3+1/3-1/4+…+1/2012-1/2013`
`⇒C/2=1-1/2013`
`⇒C/2=2012/2013`
`⇒C=4024/2013`
`⇒B=4024/{4024/2013}`
`⇒B=2013`