Question

Giải giúp mik bài này với mik sắp thi rồi: 1/2x3+1/3x4+...+1/x(x+1)=2/5

Answer 1

\(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{x\left(x+1\right)}=\frac{2}{5}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{2}{5}\)

\(\Rightarrow\frac{1}{2}-\frac{1}{x+1}=\frac{2}{5}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{2}-\frac{2}{5}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{10}\)

=> x+1=10

=>x=9

Answer 2

cacs bạn 

Answer 3

1/2x3+1/3x4+...+1/x(x+1)=2/5

=> 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/x - 1/x + 1 = 2/5

=> 1/2 - 1/x + 1 = 2/5

=> 1/x + 1 = 1/10

=> x + 1 = 10

=> x = 9

Answer 4

9 là đúng đó

Answer 5

https://youtu.be/7-8xWXBRWpw

Answer 6

\(\frac{1}{2.3}\)+\(\frac{1}{3.4}\)+ ... + \(\frac{1}{x\left(x+1\right)}\)= \(\frac{2}{5}\)

<=> \(\frac{1}{2}\)- \(\frac{1}{3}\)+ \(\frac{1}{3}\) - \(\frac{1}{4}\) + ... + \(\frac{1}{x}\) - \(\frac{1}{x+1}\) = \(\frac{2}{5}\)

<=> \(\frac{1}{2}\) - \(\frac{1}{x+1}\) = \(\frac{2}{5}\)

<=>              \(\frac{1}{x+1}\)= \(\frac{1}{2}\)- \(\frac{2}{5}\) = \(\frac{5}{10}\)- \(\frac{4}{10}\)= \(\frac{1}{10}\)

=> \(x+1\)\(=10\)

            <=> \(x=10-1\)

           <=> \(x=9\)

Vậy \(x=9\)

Answer 7

oh my god