Toán 1/3 +1/6 +1/10 +…+1/x*(x+1) :2=2009/2011 Tìm x biết: $\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+…+\dfrac{1}{\dfrac{x\times(x+1)}{2}}=\dfrac{2009}{20 23/07/2021 By Nevaeh 1/3 +1/6 +1/10 +…+1/x*(x+1) :2=2009/2011 Tìm x biết: $\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+…+\dfrac{1}{\dfrac{x\times(x+1)}{2}}=\dfrac{2009}{2011}$
Đáp án: x = 2010 Giải thích các bước giải: 1/3 + 1/6 + 1/10 + ….. + 1/x ( x + 1 ) : 2 = 2009/2011 ⇔ 2/6 + 2/12 + 2 / 20 +….. + 2/x ( x + 1 ) = 2009/2011 ⇔ 2/2 x 3 + 2/3 x 4 + 2/4 x 5 +…… + 2/ x ( x + 1 ) = 2009/2011 ⇔ 2 ( 1/2 x 3 + 1/3 x 4 + 1/4 x 5 +….. + 1/x ( x + 1 ) = 2009/2011 ⇔ 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 +…. + 1/x – 1/x + 1 = 2009/2011 : 2 ⇔ 1/2 – 1/x + 1 = 2009/4022 ⇔ 1/x + 1 = 1/2011 ⇔ x = 2010 Vậy x = 2010 Trả lời
Đáp án: x = 2010 Giải thích các bước giải: 1/3 + 1/6 + 1/10 + ….. + 1/x ( x + 1 ) : 2 = 2009/2011 ⇔ 2/6 + 2/12 + 2 / 20 +….. + 2/x ( x + 1 ) = 2009/2011 ⇔ 2/2 x 3 + 2/3 x 4 + 2/4 x 5 +…… + 2/ x ( x + 1 ) = 2009/2011 ⇔ 2 ( 1/2 x 3 + 1/3 x 4 + 1/4 x 5 +….. + 1/x ( x + 1 ) = 2009/2011 ⇔ 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 +…. + 1/x – 1/x + 1 = 2009/2011 : 2 ⇔ 1/2 – 1/x + 1 = 2009/4022 ⇔ 1/x + 1 = 1/2011 ⇔ x = 2010 Vậy x = 2010 Trả lời