Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(\frac{2016+x}{x}+\frac{2520+x}{x}+\frac{3024+x}{x}=2523\)
\(\Leftrightarrow\frac{2016+x+2520+x+3024+x}{x}=2523\)
\(\Leftrightarrow\frac{7560+3x}{x}=\frac{2523x}{x}\)Khử mẫu : \(7560+3x=2523x\)
\(\Leftrightarrow7560=2520x\Leftrightarrow x=3\)
\(\frac{2016+x}{x}+\frac{2520+x}{x}+\frac{3024+x}{x}=\frac{2016}{x}+\frac{x}{x}+\frac{2520}{x}+\frac{x}{x}+\frac{3024}{x}+\frac{x}{x}\)
\(=\frac{2016+2520+3024}{x}+3\)
\(=\frac{7560}{x}+3\)
\(\frac{7560}{x}+3=2523\)
\(\frac{7560}{x}=2520\)
\(x=\frac{7560}{2520}\)
\(x=3\)
Ta có: \(\frac{x-2019}{2018}+\frac{x-2018}{2017}=\frac{x-2017}{2016}+\frac{x-2016}{2015}\)
\(\Leftrightarrow\left(\frac{x-2019}{2018}+1\right)+\left(\frac{x-2018}{2017}+1\right)=\left(\frac{x-2017}{2016}+1\right)+\left(\frac{x-2016}{2015}+1\right)\)
\(\Leftrightarrow\frac{x-1}{2018}+\frac{x-1}{2017}=\frac{x-1}{2016}+\frac{x-1}{2015}\)
\(\Leftrightarrow\frac{x-1}{2018}+\frac{x-1}{2017}-\frac{x-1}{2016}-\frac{x-1}{2015}=0\)
\(\Leftrightarrow\left(x-1\right)\left(\frac{1}{2018}+\frac{1}{2017}-\frac{1}{2016}-\frac{1}{2015}\right)=0\)
\(\Leftrightarrow x-1=0\)( vì \(\frac{1}{2018}+\frac{1}{2017}-\frac{1}{2016}-\frac{1}{2015}\ne0\))
\(\Leftrightarrow x=1\)
Vạy x=1
Sửa đề \(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+...+\frac{2}{x\left(x+1\right)}=\frac{2015}{2016}\)
\(\Leftrightarrow\frac{2}{6}+\frac{2}{12}+\frac{2}{20}+..+\frac{2}{x\left(x+1\right)}=\frac{2015}{2016}\)
\(\Leftrightarrow\frac{2}{2.3}+\frac{2}{3.4}+\frac{2}{4.5}+..+\frac{2}{x\left(x+1\right)}=\frac{2015}{2016}\)
\(\Leftrightarrow2\cdot\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2015}{2016}\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2015}{2016}\div2\)
\(\Leftrightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2015}{4032}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2015}{4032}\Leftrightarrow\frac{1}{x+1}=\frac{1}{4032}\)
\(\Leftrightarrow x+1=4032\Rightarrow x=4031\)
Ta có: \(1\times\frac{1}{15}\times1\frac{1}{16}\times1\frac{1}{17}\times......\times1\frac{1}{2016}\times1\frac{1}{2017}\)
\(=\frac{1}{15}\times\frac{17}{16}\times\frac{18}{17}\times......\times\frac{2017}{2016}\times\frac{2018}{2017}\)
\(=\frac{1}{15}\times\frac{2018}{16}\)
\(=\frac{1009}{8\times15}\)
\(=\frac{1009}{120}\)
Mình nghĩ đề bài của bạn bị nhầm ở chỗ \(1\frac{1}{15}\)thành \(1\times\frac{1}{15}\)
Nhưng không sao bạn ạ
Vẫn giải được
Câu b:
\(\frac{21}{8}:\frac{5}{6}+\frac{1}{2}:\frac{5}{6}\)
= \(\frac{63}{20}+\frac{3}{5}\)
= \(\frac{15}{4}\)
\(\left(\frac{21}{8}+\frac{1}{2}\right):\frac{5}{6}\)
\(\frac{25}{8}:\frac{5}{6}\)
\(\frac{25}{8}.\frac{6}{5}\)
\(\frac{30}{8}\)
\(\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)\times...\times\left(1-\frac{1}{2015}\right)\times\left(1-\frac{1}{2016}\right)\)
\(=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\times...\times\frac{2014}{2015}\times\frac{2015}{2016}\)
\(=\frac{1}{2016}\)
Giải : Ta có (1-1/2)*(1-1/3)*(1-1/4)*....*(1-1/2015)*(1-1/2016)
= 1* -(1/2+1/3+1/4+....+1/2015+1/2016)
= 1* - (1/2+1/2016 +1/3+1/2015 +...+1/1007)
= 1* -(1/2033134)
= -1/2033134
\(\Rightarrow\frac{2016}{x}+\frac{x}{x}+\frac{2520}{x}+\frac{x}{x}+\frac{3024}{x}+\frac{x}{x}=2523\)
\(\Rightarrow\frac{2016}{x}+\frac{2520}{x}+\frac{3024}{x}=2520\)
\(\Rightarrow\frac{1}{x}\left(2016+2520+3024\right)=2520\)
\(\Rightarrow x=3\)
bài này đơn giản thôi!! x=3 . Vì không biết viết phân số nên tớ ko trả lời kèm lời giải được !! muốn biết thì hỏi lại tớ nhá !!