Tham khảo
Sửa:`\frac{4}{789}→\frac{4}{798}`
Đặt `A=\frac{4}{30}+\frac{4}{70}+...+\frac{4}{798}`
`⇒A=\frac{2}{15}+\frac{2}{35}+...+\frac{2}{399}`
`⇒A=\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{19.21}`
`⇒A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}`
`⇒A=\frac{1}{3}-\frac{1}{21}`
`⇒A=\frac{2}{7}`
Giải thích
Áp dụng `\frac{2}{n(n+2)}=\frac{1}{n}-\frac{1}{n+2}( n\ne 0,-2)`
`\text{©CBT}`
