\(\frac{1}{3}\) + \(\frac{1}{6}\) + \(\frac{1}{10}\) + ... + \(\frac{1}{x\left(x+1\right):2}\)

= \(\left(1-\frac{1}{2018}\right)-\frac{1}{2018}\) 

= \(\frac{2017}{2018}-\frac{1}{2018}\)

= \(\frac{2016}{2018}=\frac{1008}{1009}\)

1/2.(1/3+1/6+1/10+...+1/x(x+1))=1/2.2016/2018

1/6+1/12+1/20+...+1/x(x+1)=504/1009

1/2.3+1/3.4+1/4.5+...+1/x(x+1)=504/1009

1/2-1/3+1/3-1/4+1/4-1/5+...+1/x-1/x+1=504/1009

1/2-1/x+1=504/1009

x-1/2(x+1)=504/1009

-> 1009(x-1)=504.2(x+1)

1009x-1009=1008x+1008

1009x-1008x=1008+1009

->x=2017

\(A=\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\left(x+1\right):2}=\frac{2016}{2018}\)
\(A=\frac{1}{2\left(2+1\right):2}+\frac{1}{3\left(3+1\right):2}+...+\frac{1}{x\left(x+1\right):2}\)
\(A=\frac{1}{2\left(2+1\right)}\cdot2+\frac{1}{3\left(3+1\right)}\cdot2+...+\frac{1}{x\left(x+1\right)}.2=\frac{2016}{2018}\)
\(A=2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2016}{2018}\)
\(A=2\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2016}{2018}\)
\(A=1-\frac{1}{x+1}=\frac{2016}{2018}\)
\(\Rightarrow\frac{1}{x+1}=1-\frac{2016}{2018}=\frac{1}{1009}\)
\(\Rightarrow x+1=1009\Rightarrow x=1008\)

\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{1}{x\cdot\left(x+1\right):2}=\dfrac{2016}{2018}\\ \dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{20}+...+\dfrac{2}{x\cdot\left(x+1\right)}=\dfrac{2016}{2018}\\ 2\cdot\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{x\cdot\left(x+1\right)}\right)=\dfrac{2016}{2018}\\ 2\cdot\left(\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+...+\dfrac{1}{x\cdot\left(x+1\right)}\right)=\dfrac{2016}{2018}\\ 2\cdot\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{x}-\dfrac{1}{x+1}\right)=\dfrac{2016}{2018}:2\\ \dfrac{1}{2}-\dfrac{1}{x+1}=\dfrac{1008}{2018}\\ \dfrac{1}{x+1}=\dfrac{1}{2}-\dfrac{1008}{2018}\\ \dfrac{1}{x+1}=\dfrac{1}{2018}\\ \Leftrightarrow x+1=2018\\ x=2018-1\\ x=2017\)

help me

\(a)\) Ta có : 

\(VP=\frac{2018}{1}+\frac{2017}{2}+\frac{2016}{3}+...+\frac{2}{2017}+\frac{1}{2018}\)

\(VP=\left(\frac{2018}{1}-1-...-1\right)+\left(\frac{2017}{2}+1\right)+\left(\frac{2016}{3}+1\right)+...+\left(\frac{2}{2017}+1\right)+\left(\frac{1}{2018}+1\right)\)

\(VP=1+\frac{2019}{2}+\frac{2019}{3}+...+\frac{2019}{2017}+\frac{2019}{2018}\)

\(VP=2019\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2017}+\frac{1}{2018}+\frac{1}{2019}\right)\)

Lại có : 

\(VT=\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2019}\right).x\)

\(\Rightarrow\)\(x=2019\)

Vậy \(x=2019\)

Chúc bạn học tốt ~ 

cái đề j mk khó hỉu vậy viết đòang hoàng xem nào

Tìm số tự nhiên x biết

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{1}{x\cdot\left(x+1\right):2}=\frac{2016}{2018}\)

Câu a:

C = 1 + 5^2 + 5^4 + 5^6 + ... + 5^ 2018

5^2C= 5^2 + 5^4 + ...+ 5^ 2020

25C - C = 5^2 + 5^4 + ...+ 5^ 2020 - ( 1 + 5^2 + ... + 5^ 2018)

24C = (5^2 - 5^2) +...+(5^2018 - 5^2018) + (5^2020 - 1)

24C = 0 + 0 +...+ 5^2020 - 1

C = (5^2020 - 1)/24

Câu b:

D = 2 x 4 + 4 x 6 + 6 x 8 +...+ 2016 x 2018

6D = 2.4.6 + 4.6.6 + ... + 2016.2018.6

6D = 2.4.6 + 4.6.(8 - 2) + 6.8.(10 - 4) +...+2016.2018.(2020-2014)

6D = 2.4.6 + 4.6.8 - 2.4.6 + 6.8.10 - 4.6.8 +...+2016.2018.2020 - 2014.2016.2018

6D = 2016.2018.2020

D= 2016.2018.2020: 6

D = (2016 : 6).(2018.2020)

D = 336.4076360

D = 136956960

=1+(2-3-4+5)+(6-7-8+9)+(10-11-12+13)+......+(2014-2015-2016-2017)+2018                                                                                                                       có 504 nhóm                                                                                                                                                         =1+  0  +     0       +0         +..........+    0        +2018                                                                                                                                               có 504 số 0                                                                                                                                                                    =  2019       

Minh lam ra bang 3027 

Co noi voi minh la dung

Chac chan 100%

2107 hoặc 1 đáp án khác

bang 2017