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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
\(\frac{7}{x}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{41.45}=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}+\left(\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{41.45}\right)=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+...+\frac{1}{41}-\frac{1}{45}\right)=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}+\left(\frac{1}{5}-\frac{1}{45}\right)=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}+\frac{8}{45}=\frac{29}{45}\)
\(\Rightarrow\frac{7}{x}=\frac{29}{45}-\frac{8}{45}\)
\(\Rightarrow\frac{7}{x}=\frac{7}{15}\)
\(\Rightarrow x=15\)
Vậy x = 15
_Chúc bạn học tốt_
g: \(=-457+237+23-123=-220-100=-320\)
h: \(=\left(1-3\right)+\left(5-7\right)+...+\left(41-43\right)+\left(45-47\right)\)
\(=\left(-2\right)+\left(-2\right)+...+\left(-2\right)+\left(-2\right)\)
\(=-2\cdot12=-24\)
i: \(=173+27-46-54-19=200-100-19=100-19=81\)
k: \(=-52+82+49-15+13-36\)
\(=30+34-23\)
=30+11
=41
l: \(=\left(3-5\right)+\left(7-9\right)+\left(11-13\right)+\left(15-17\right)\)
\(=\left(-2\right)+\left(-2\right)+\left(-2\right)+\left(-2\right)\)
=-8
m: \(=\left(1-2\right)+\left(3-4\right)+...+\left(2001-2002\right)+2003\)
\(=2003-1-1-...-1\)
\(=2003-1001=1002\)
n:Số số hạng là:
\(\left[\left(-51\right)-\left(-99\right)\right]:1+1=49\left(số\right)\)
Tổng là \(\left(-51-99\right)\cdot\dfrac{49}{2}=-3675\)
o: \(=-62-38+1523-2523-92\)
\(=-100+1000-92=900-92=808\)
=>x-(1/5-1/9+1/9-1/13+...+1/41-1/45)=37/45
=>x-8/45=37/45
=>x=1