Tham khảo
` \frac{0,25a}{22}=\frac{27}{6}+\frac{27}{18}+...+\frac{27}{1260}+\frac{27}{1386}`
`⇒\frac{0,25a}{22}=\frac{9}{2}+\frac{9}{6}+...+\frac{9}{420}+\frac{9}{462}`
`⇒\frac{0,25a}{22}=9(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{420}+\frac{1}{462}`
`⇒\frac{0,25a}{22}=9×(\frac{1}{1×2}+\frac{1}{2×3}+\frac{1}{20×21}+\frac{1}{21×22}`
Áp dụng `\frac{1}{n(n+1)}=\frac{1}{n}-\frac{1}{n+1}`
`⇒\frac{0,25a}{22}=9×(1-\frac{1}{2}+\frac{1}{2}+...+\frac{1}{21}-\frac{1}{22})`
`⇒\frac{0,25a}{22}=9×(1-\frac{1}{22}`
`⇒\frac{0,25a}{22}=9×\frac{21}{22}`
`⇒\frac{0,25a}{22}=\frac{189}{22}`
`⇔0,25a=189 `
`⇒a=189÷0,25`
`⇒a=756`
Vậy `a=756`
