Toán Tìm `x` biết `1/21+1/77+1/165+…+1/(n^2+4n)=56/673`. 16/07/2021 By Ximena Tìm `x` biết `1/21+1/77+1/165+…+1/(n^2+4n)=56/673`.
ta có: $\frac{1}{21}$ + $\frac{1}{77}$ + $\frac{1}{165}$ +…+ $\frac{1}{n²+4n}$ + $\frac{56}{673}$ ⇔ $\frac{1}{3.7}$ + $\frac{1}{7.11}$ + $\frac{1}{11.5}$ +…+ $\frac{1}{n(n+4)}$ + $\frac{56}{673}$ ⇔ $\frac{4}{3.7}$ + $\frac{4}{7.11}$ + $\frac{4}{11.5}$ +…+ $\frac{4}{n(n+4)}$ + $\frac{4.56}{673}$ ⇔ $\frac{1}{3}$ – $\frac{1}{7}$ + $\frac{1}{7}$ – $\frac{1}{11}$ +…+ $\frac{1}{n}$ = $\frac{1}{n+4}$ = $\frac{224}{673}$ ⇔ $\frac{1}{3}$ – $\frac{1}{n+4}$ = $\frac{224}{673}$ ⇔ $\frac{1}{n+4}$= $\frac{1}{2019}$ ⇔ n = 2015 ????#ɷįᵰƫ_ᵭậᵱ_ɕɧᶏɨ ???? Trả lời
`1/21 + 1/77 + 1/165 + … + 1/(n^2+4n) = 56/673` `⇒ 1/3.7 + 1/7.11 + 1/11.15 + … + 1/(n(n+4)) = 56/673` `⇒ 1/3 – 1/7 + 1/7 – 1/11 + 1/11 – 1/15 + … + 1/n – 1/(n+4) = 56/673 xx 4` `⇒ 1/3 – 1/(n+4) = 224/673` `⇒ 1/(n+4) = 1/3 – 224/673` `⇒ 1/(n+4) = 1/2019` `⇒ n + 4 = 2019` `⇒ n = 2015` Vậy `n = 2015` Trả lời
ta có: $\frac{1}{21}$ + $\frac{1}{77}$ + $\frac{1}{165}$ +…+ $\frac{1}{n²+4n}$ + $\frac{56}{673}$
⇔ $\frac{1}{3.7}$ + $\frac{1}{7.11}$ + $\frac{1}{11.5}$ +…+ $\frac{1}{n(n+4)}$ + $\frac{56}{673}$
⇔ $\frac{4}{3.7}$ + $\frac{4}{7.11}$ + $\frac{4}{11.5}$ +…+ $\frac{4}{n(n+4)}$ + $\frac{4.56}{673}$
⇔ $\frac{1}{3}$ – $\frac{1}{7}$ + $\frac{1}{7}$ – $\frac{1}{11}$ +…+ $\frac{1}{n}$ = $\frac{1}{n+4}$ = $\frac{224}{673}$
⇔ $\frac{1}{3}$ – $\frac{1}{n+4}$ = $\frac{224}{673}$
⇔ $\frac{1}{n+4}$= $\frac{1}{2019}$
⇔ n = 2015
????#ɷįᵰƫ_ᵭậᵱ_ɕɧᶏɨ ????
`1/21 + 1/77 + 1/165 + … + 1/(n^2+4n) = 56/673`
`⇒ 1/3.7 + 1/7.11 + 1/11.15 + … + 1/(n(n+4)) = 56/673`
`⇒ 1/3 – 1/7 + 1/7 – 1/11 + 1/11 – 1/15 + … + 1/n – 1/(n+4) = 56/673 xx 4`
`⇒ 1/3 – 1/(n+4) = 224/673`
`⇒ 1/(n+4) = 1/3 – 224/673`
`⇒ 1/(n+4) = 1/2019`
`⇒ n + 4 = 2019`
`⇒ n = 2015`
Vậy `n = 2015`