tính tổng: S= 1/10 + 1/40 + 1/88 + 1/154 + 1/238 + 1/340 V= 1/3 + 1/9 + 1/27+…..+ 1/729 + 1/ 2187 07/11/2021 Bởi Katherine tính tổng: S= 1/10 + 1/40 + 1/88 + 1/154 + 1/238 + 1/340 V= 1/3 + 1/9 + 1/27+…..+ 1/729 + 1/ 2187
`S = 1/10 + 1/40 + 1/88 + 1/154 + 1/238 + 1/340` `= 1/(2×5) + 1/(5×8) + 1/(8×11) + 1/(11×14) + 1/(14×17) + 1/(17×20))` `= 1/3 × (3/(2×5) + 3/(5×8) + 3/(11×14) + 3/(14×17) + 3/(17×20))` `= 1/3 × (1/2 – 1/5 + 1/5 – 1/8 + 1/8 – 1/11 + 1/11 -1/14 + 1/14 – 1/17 + 1/17 – 1/20)` `= 1/3 × (1/2 – 1/20)` `= 1/3 × (10/20 – 1/20)` `= 1/3 × 9/20 = 3/20` `V = 1/3 + 1/9 + 1/27 +…+ 1/729 + 1/2187` `⇒ 1/3 V = 1/3 × (1/3 + 1/9 + 1/27 +…+ 1/729 + 1/2187)` `⇒ 1/3 V = 1/9 + 1/27 + 1/81 +….+ 1/2187 + 1/6561` `⇒ V – 1/3V = (1/3 + 1/9 + 1/27 +…+ 1/729 + 1/2187) – (1/9 + 1/27 + 1/81 +….+ 1/2187 + 1/6561)` `⇒ 2/3 V = 1/3 – 1/6561` `⇒ 2/3 V = 2187/6561 – 1/6561` `⇒ 2/3 V = 2186/6561` `⇒ V = 2186/6561 : 2/3` `⇒ V = 2186/6561 × 3/2 = 1093/2187` Bình luận
`S = 1/10 + 1/40 + 1/88 + 1/154 + 1/238 + 1/340`
`= 1/(2×5) + 1/(5×8) + 1/(8×11) + 1/(11×14) + 1/(14×17) + 1/(17×20))`
`= 1/3 × (3/(2×5) + 3/(5×8) + 3/(11×14) + 3/(14×17) + 3/(17×20))`
`= 1/3 × (1/2 – 1/5 + 1/5 – 1/8 + 1/8 – 1/11 + 1/11 -1/14 + 1/14 – 1/17 + 1/17 – 1/20)`
`= 1/3 × (1/2 – 1/20)`
`= 1/3 × (10/20 – 1/20)`
`= 1/3 × 9/20 = 3/20`
`V = 1/3 + 1/9 + 1/27 +…+ 1/729 + 1/2187`
`⇒ 1/3 V = 1/3 × (1/3 + 1/9 + 1/27 +…+ 1/729 + 1/2187)`
`⇒ 1/3 V = 1/9 + 1/27 + 1/81 +….+ 1/2187 + 1/6561`
`⇒ V – 1/3V = (1/3 + 1/9 + 1/27 +…+ 1/729 + 1/2187) – (1/9 + 1/27 + 1/81 +….+ 1/2187 + 1/6561)`
`⇒ 2/3 V = 1/3 – 1/6561`
`⇒ 2/3 V = 2187/6561 – 1/6561`
`⇒ 2/3 V = 2186/6561`
`⇒ V = 2186/6561 : 2/3`
`⇒ V = 2186/6561 × 3/2 = 1093/2187`