Toán 1/6 + 1/12+ 1/20+ 1/30+…+ 1/x nhân ( x+1)=2011/4026 07/09/2021 By Nevaeh 1/6 + 1/12+ 1/20+ 1/30+…+ 1/x nhân ( x+1)=2011/4026
Đáp án: `x = 2012` Giải thích các bước giải: `1/6 + 1/12 + 1/20 + 1/30 + … + 1/x.(x + 1) = 2011/4026` `1/(2X3) + 1/(3X4) + 1/(4X5) + 1/(5X6) + … + 1/(xX (x + 1)) = 2011/4026` `1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + 1/5 – 1/6 + … + 1/x – 1/(x+1) = 2011/4026` `1/2 – 1/(x+1) = 2011/4026` `1/(x+1) = 1/2 – 2011/4026` `1/(x+1) = 2013/4026 – 2011/4026` `1/(x+1) = 1/2013` `x + 1 = 2013` `x = 2013 – 1` `x = 2012` Trả lời
Ta có: $\dfrac{1}{6}$ $+$ $\dfrac{1}{12}$ $+$ $…$ $+$ $\dfrac{1}{x.( x+1)}$ $=$ $\dfrac{2011}{4026}$ ⇔ $\dfrac{1}{2.3}$ $+$$\dfrac{1}{3.4}$ $+$ $…$ $+$ $\dfrac{1}{x. (x+1)}$ ⇔ $\dfrac{1}{2}$ $-$ $\dfrac{1}{3}$ $+$ $\dfrac{1}{3}$ $-$ $\dfrac{1}{4}$ $+$ $….$ $\dfrac{1}{x}$ $-$ $\dfrac{1}{x+ 1}$ $=$ $\dfrac{2011}{4026}$ ⇔ $\dfrac{1}{2}$ $-$ $\dfrac{1}{x+ 1}$ $=$ $\dfrac{2011}{4026}$ ⇔ $\dfrac{1}{x+1}$ $=$ $\dfrac{1}{2}$ $-$ $\dfrac{2011}{4026}$ ⇔ $\dfrac{1}{x+1}$ $=$ $\dfrac{2}{4026}$ ⇔ $\dfrac{1}{x+1}$ $=$ $\dfrac{1}{2013}$ ⇔ $x$ $+$ $1$ $=$ $2013$ ⇔ $x$ $=$ $2013$ $-$ $1$ ⇔ $x$ $=$ $2012$ Vậy $x$ $=$ $2012$ Chúc bạn học tốt! Trả lời
Đáp án: `x = 2012`
Giải thích các bước giải:
`1/6 + 1/12 + 1/20 + 1/30 + … + 1/x.(x + 1) = 2011/4026`
`1/(2X3) + 1/(3X4) + 1/(4X5) + 1/(5X6) + … + 1/(xX (x + 1)) = 2011/4026`
`1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + 1/5 – 1/6 + … + 1/x – 1/(x+1) = 2011/4026`
`1/2 – 1/(x+1) = 2011/4026`
`1/(x+1) = 1/2 – 2011/4026`
`1/(x+1) = 2013/4026 – 2011/4026`
`1/(x+1) = 1/2013`
`x + 1 = 2013`
`x = 2013 – 1`
`x = 2012`
Ta có:
$\dfrac{1}{6}$ $+$ $\dfrac{1}{12}$ $+$ $…$ $+$ $\dfrac{1}{x.( x+1)}$ $=$ $\dfrac{2011}{4026}$
⇔ $\dfrac{1}{2.3}$ $+$$\dfrac{1}{3.4}$ $+$ $…$ $+$ $\dfrac{1}{x. (x+1)}$
⇔ $\dfrac{1}{2}$ $-$ $\dfrac{1}{3}$ $+$ $\dfrac{1}{3}$ $-$ $\dfrac{1}{4}$ $+$ $….$ $\dfrac{1}{x}$ $-$ $\dfrac{1}{x+ 1}$ $=$ $\dfrac{2011}{4026}$
⇔ $\dfrac{1}{2}$ $-$ $\dfrac{1}{x+ 1}$ $=$ $\dfrac{2011}{4026}$
⇔ $\dfrac{1}{x+1}$ $=$ $\dfrac{1}{2}$ $-$ $\dfrac{2011}{4026}$
⇔ $\dfrac{1}{x+1}$ $=$ $\dfrac{2}{4026}$
⇔ $\dfrac{1}{x+1}$ $=$ $\dfrac{1}{2013}$
⇔ $x$ $+$ $1$ $=$ $2013$
⇔ $x$ $=$ $2013$ $-$ $1$
⇔ $x$ $=$ $2012$
Vậy $x$ $=$ $2012$
Chúc bạn học tốt!