\(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{63}+...+\frac{1}{\left(x+1\right)\left(x+4\right)}=\frac{199}{400}\)(ĐK \(x\ne-1;-4\))
=> \(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{\left(x+1\right)\left(x+4\right)}=\frac{199}{400}\)
=> \(\frac{1}{2}\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{\left(x+1\right)\left(x+4\right)}\right)=\frac{199}{400}\)
=> \(\frac{1}{2}\left(1-\frac{1}{x+4}\right)=\frac{199}{400}\)
=> \(1-\frac{1}{x+4}=\frac{199}{400}:\frac{1}{2}=\frac{199}{200}\)
=> \(\frac{1}{x+4}=1-\frac{199}{200}=\frac{1}{200}\)
=> x + 4 = 200 => x = 196(tm)
Ta có
1/3 = 1/1 x 3
1/15 = 1/3 x 5
1/35 = 1/5 x 7
.....
1/(x + 1 ) x ( x + 4 )
\(\Rightarrow\)1 - 1/3 + 1/3 - 1/5 +1/5 - 1/7 +............+ 1/( x + 1 ) - 1/( x + 4) = 199/400
\(\Rightarrow\)1 - 1/( x + 4 ) = 199/400
\(\Rightarrow\)1/(x + 4 ) = 1 - 199/400
\(\Rightarrow\)1/(x + 4 ) = 201/400
còn lại bạn tự làm nha
