Question

c) 1/3.4 + 1/4,5 + 1/5.6 + .... + 1/x.(x + 1) = 3/10 và x thuộc N

Answer 1

\(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{x\cdot\left(x+1\right)}=\frac{3}{10}\)

\(\Rightarrow\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{3}{10}\)

\(\Rightarrow\frac{1}{3}-\frac{1}{x+1}=\frac{3}{10}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{3}-\frac{3}{10}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{30}\)

\(\Rightarrow x=30-1\)

\(\Rightarrow x=29\)

vậy: \(x=29\)