=>x-(1/5-1/9+1/9-1/13+...+1/41-1/45)=37/45

=>x-8/45=37/45

=>x=1

Gọi A=4/5.9+4/9.13+4/13.17+...+4/41.45

4.A=4.4/5.9+4.4/9.13+...+4.4/41.45

   A=4/5-4/9+4/9-4/13+...+4/41-4/45

   A=4/5-4/45

   A=32/45

Vậy 4/5.9+4/9.13+...+4/41.45=32/45

Mình ko biết nha.Mình cũng ko biết làm

\(4.S=\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{41.45}\)

\(4S=\frac{1}{5}-\frac{1}{6}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{41}-\frac{1}{45}\)

\(4S=\frac{1}{5}-\frac{1}{45}=\frac{8}{45}\)

\(S=\frac{8}{45}:4=\frac{2}{45}\)

\(S=\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+...+\frac{1}{41.45}\)

\(\Rightarrow4S=\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{41.45}\)

\(\Rightarrow4S=\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{41}-\frac{1}{45}\)

\(\Rightarrow4S=\frac{1}{5}-\frac{1}{45}=\frac{8}{45}\Rightarrow S=\frac{8}{45}:4=\frac{2}{45}\)

~ Hok tốt ~

B=1/1*5+1/5*9+...+1/41*45=1/4(4/1*5+4/5*9+...+4/41*45)=1/4(1-1/5+1/5-1/9+...+1/41-1/45)=1/4(45/45-1/45)=1/4*44/45=11/45

`a,`

`31/23-(7/32+8/23)`

`=31/23-7/32-8/23`

`=(31/23-8/23)-7/32`

`=1-7/32=25/32`

`b,`

`38/45-(8/45-17/51-3/11)`

`=38/45-8/45+17/51+3/11`

`= (38/45-8/45)+17/51+3/11`

`=2/3+17/51+3/11`

`=1+3/11=14/11`

`c,`

`(1/3+12/67+13/41)-(79/67-28/41)`

`= 1/3+12/67+13/41-79/67+28/41`

`= 1/3+(12/67-79/67)+(13/41+28/41)`

`= 1/3+(-1)+1=1/3+(-1+1)=1/3+0=1/3`

`d,`

`1/5+(-1/6)+1/7+(-1/8)+1/9+1/8+(-1/7)+1/6+(-1/5)`

`= (1/5+ -1/5)+(-1/6+1/6)+(1/7+ -1/7)+(-1/8 +1/8)+1/9`

`= 0+0+0+0+1/9=1/9 .`