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x + 4/5.9 + 4/9.13 + ... + 4/41.45 = -37/45
<=> x + 1/5 - 1/9 + 1/9 - 1/13 + ... + 1/41 - 1/45= -37/45
<=> x + 1/5 - 1/45 = -37/45
<=> x + 9/45 = -36/45
<=>x= -45/45=-1
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
Tìm x
\(\dfrac{x}{5}\)=\(\dfrac{x+6}{15}\)
\(\Rightarrow\)\(\dfrac{3x}{15}\)=\(\dfrac{x+6}{15}\)
\(\Rightarrow\)3x = x+6
\(\Rightarrow\)2x=6
\(\Rightarrow\)x=3
TÍNH TỔNG S
S=\(\dfrac{4}{1.5}+\dfrac{4}{5.9}+\dfrac{4}{9.13}+...+\dfrac{4}{17.21}\)
S=\(1-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{17}-\dfrac{1}{21}\)
S= \(1-\dfrac{1}{21}\)
S= \(\dfrac{20}{21}\)
Tìm x:
\(\dfrac{x}{5}=\dfrac{x+6}{15}=>\dfrac{3x}{15}=\dfrac{x+6}{15}\)
=> 3x = 6 + x
=> 2x = 6
=> x = 3
Tính tổng S:
\(S=\dfrac{4}{1.5}+\dfrac{4}{5.9}+\dfrac{4}{9.13}+...+\dfrac{4}{17.21}\)
\(S=\dfrac{4}{1}-\dfrac{4}{5}+\dfrac{4}{5}-\dfrac{4}{9}+\dfrac{4}{9}-\dfrac{4}{13}+...+\dfrac{4}{17}-\dfrac{4}{21}\)
\(S=4-\dfrac{4}{21}\)
\(S=\dfrac{80}{21}\)
\(A=\dfrac{4}{1\cdot5}+\dfrac{4}{5\cdot9}+\dfrac{4}{9\cdot13}+...+\dfrac{4}{17\cdot21}< 1\)
\(A=\dfrac{4}{4}\cdot\left(\dfrac{1}{1\cdot5}+\dfrac{1}{5\cdot9}+\dfrac{1}{9\cdot13}+...+\dfrac{1}{17\cdot21}\right)< 1\)
\(A=\dfrac{1}{1}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{17}-\dfrac{1}{21}< 1\)
\(A=1-\dfrac{1}{21}< 1\) (đúng) (đpcm).
\(x+\frac{3}{5.9}+\frac{3}{9.13}+\frac{3}{13.17}+...+\frac{4}{41.45}=-\frac{37}{45}\)
\(\Leftrightarrow x+3\left(\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+...+\frac{1}{41.45}\right)=-\frac{37}{45}\)
\(\Leftrightarrow x+\frac{3}{4}\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{13}+\frac{1}{13}-\frac{1}{17}+...+\frac{1}{41}-\frac{1}{45}\right)=-\frac{37}{45}\)
\(\Leftrightarrow x+\frac{3}{4}\left(\frac{1}{5}-\frac{1}{45}\right)=-\frac{37}{45}\)
\(\Leftrightarrow x+\frac{3}{4}.\frac{8}{45}=-\frac{37}{45}\)
\(\Leftrightarrow x+\frac{2}{15}=-\frac{37}{45}\)
\(\Leftrightarrow x=-\frac{43}{45}\)
bài này mà cũng đăng dễ ẹc
x + 4/5.9 + 4/9.13 + 4/13.17 + ... + 4/41.45 =-37/45
x+( 1/5 - 1/9 +1/9 - 1/13 + 1/13 - 1/17 + ... + 1/41 - 1/45 )= -37/45
x+ (1/5 - 1/45 )=-37/45
x+8/45 = -37 / 45
x=-37/45 -8/45
x=-45/45=-1
10)\(\left(\dfrac{2x}{5}-1\right):\left(-5\right)=\dfrac{1}{4}\)
\(\dfrac{2x}{5}-1=\dfrac{1}{4}.\left(-5\right)\)
\(\dfrac{2x}{5}-1=-\dfrac{5}{4}\)
\(\dfrac{2x}{5}=-\dfrac{5}{4}+1\)
\(\dfrac{2x}{5}=-\dfrac{1}{4}\)
\(\dfrac{8x}{20}=-\dfrac{5}{20}\)
\(\Leftrightarrow8x=-5\)
\(\Rightarrow x=-5:8\)
\(x=-\dfrac{5}{8}\)
12)\(\left(3\dfrac{1}{4}:x\right).\left(-1\dfrac{1}{4}\right)=-\dfrac{5}{3}-\dfrac{5}{6}\)
\(\left(\dfrac{13}{4}:x\right).\left(-\dfrac{5}{4}\right)=-\dfrac{5}{2}\)
\(\dfrac{13}{4}:x=-\dfrac{5}{2}:\left(-\dfrac{5}{4}\right)\)
\(\dfrac{13}{4}:x=2\)
\(x=\dfrac{13}{4}:2\)
\(x=\dfrac{13}{8}\)
\(x+\dfrac{4}{5.9}+\dfrac{4}{9.13}+...+\dfrac{4}{41.45}=-\dfrac{37}{45}\\ x+\left(\dfrac{1}{5}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{13}+...+\dfrac{1}{44}-\dfrac{1}{45}\right)=-\dfrac{37}{45}\\ x+\left(\dfrac{1}{5}-\dfrac{1}{45}\right)=-\dfrac{37}{45}\\ x+\dfrac{8}{45}=-\dfrac{37}{45}\\ x=-\dfrac{37}{45}-\dfrac{8}{45}\\ x=-1\)
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