theo đề bài ta có:
\(x+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{41}-\frac{1}{45}=\frac{-37}{45}\)
\(x+\left(\frac{1}{5}-\frac{1}{45}\right)=\frac{-37}{45}\)
\(x+\frac{8}{45}=\frac{-37}{45}\)
\(x=\frac{-37}{45}-\frac{8}{45}\)
\(x=\frac{-45}{45}=1\)
đặt A=4/5.9+4/9.13+4/13.17+...+4/41.45
=1/5-1/9+1/9-1/13+1/13-1/17+...+1/41-1/45
=1/5-1/45
=8/45
suy ra x+8/45=-37/45
suy ra x=-1
x+ 1/5.9 + ... + 1/41+ 1/45 = -37/45
x + 1/5 - 1/9 + 1/9 - ......+ 1/41 - 1/45 = -37/45
x+ 1/5 - 1/45 = -37 45
x+ 8/45 =-37/45
x = -37 /45 - 8/45
x = -1
x+(1/4-1/9+1/9-1/14+....+4/41-4/45)=-37/45
x+(1/4-1/45)=-37/45
x+8/45=-37/45
x=-37/45-8/45
x=29/45
Trả lời,..................
X=-1
..................học tốt....................
\(\Leftrightarrow x+\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{41}-\frac{1}{45}=-\frac{37}{45}\)
\(\Leftrightarrow x+\frac{1}{5}-\frac{1}{45}=-\frac{37}{45}\)
\(\Leftrightarrow x+\frac{1}{5}-\frac{1}{45}+\frac{37}{45}=0\)
\(\Leftrightarrow x+\frac{1}{5}+\frac{36}{45}=0\)
\(\Leftrightarrow x+\frac{1}{5}+\frac{4}{5}=0\)
\(\Leftrightarrow x+1=0\)
\(\Leftrightarrow x=-1\)