tính giá trị biểu thức:
$\frac{12}{5.2.5}$+$\frac{12}{5.5.8}$+…+$\frac{12}{5.17.20}$
tính giá trị biểu thức: $\frac{12}{5.2.5}$+$\frac{12}{5.5.8}$+…+$\frac{12}{5.17.20}$
By Raelynn
By Raelynn
tính giá trị biểu thức:
$\frac{12}{5.2.5}$+$\frac{12}{5.5.8}$+…+$\frac{12}{5.17.20}$
Đặt `A= 12/(5.2.5) + 12/(5.5.8) +…+12/(5.17.20)`
`A= 12/5 ( 1/2.5 + 1/5.8 + …+1/17.20)`
`A= 4/5( 3/2.5 + 3/5.8 +…+ 3/17.20)`
`A= 4/5 ( 1/2 – 1/5 + 1/5 – 1/8+…+1/17-1/20)`
`A= 4/5 . ( 1/2 – 1/20)`
`A= 4/5 . 9/20`
`A= 9/25`
Vậy `A= 9/25`
Tham khảo
Đặt `A=\frac{12}{5.2.5}+\frac{12}{5.5.8}+…+\frac{12}{5.17.20}`
`⇒A=\frac{4}{5}.(\frac{3}{2.5}+\frac{3}{5.8}+…+\frac{3}{17.20})`
`⇒A=\frac{4}{5}.(\frac{1}{2}-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+….+\frac{1}{17}-\frac{1}{20})`
`⇒A=\frac{4}{5}.(\frac{1}{2}-\frac{1}{20})`
`⇒A=\frac{4}{5}.\frac{9}{20}`
`⇒A=\frac{9}{25}`
Giải thích
Áp dụng `\frac{3}{n(n+3)}=\frac{1}{n}-\frac{1}{n+3}(n\ne 0,-3)`
`\text{©CBT}`