Ta có:
\(\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{x.\left(x+1\right)}=\frac{432}{15}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{432}{15}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{x+1}=\frac{432}{15}\)
\(\Rightarrow\frac{1}{x+1}=\frac{1}{1}-\frac{432}{15}=-\frac{139}{5}\)
\(\Rightarrow\left(x+1\right).-139=5\Rightarrow x=\frac{-5}{139}-1=-\frac{144}{139}\)
Có thể bạn đã sai đề.
1 - 1/x+1 = 432/15
1/x+1 = 1- 432/15
\(\frac{-139}{5}\)
Ta có\(\frac{1}{1.2}+\frac{1}{2.3}+.....+\frac{1}{x\left(x+1\right)}=\frac{432}{15}\)
\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.......+\frac{1}{x-1}-\frac{1}{x}+\frac{1}{x}-\frac{1}{x+1}\)= \(\frac{432}{15}\)
\(\Leftrightarrow1-\frac{1}{x+1}=\frac{432}{15}\)
\(\Leftrightarrow\frac{1}{x+1}=-\frac{139}{5}\)
\(\Leftrightarrow-139\left(x+1\right)=5\)
x=\(\frac{-144}{139}\)
xin loi moi nguoi vi thay minh chep sai de nen moi ra ket qua nhu the cam on cac ban da giup do minh nhe
