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Đặt A là tên của biểu thức trên
2A = \(\frac{7.2}{5.9}+\frac{7.2}{9.11}+\frac{7.2}{11.13}+\frac{7.2}{13.15}+...+\frac{7.2}{2015.2017}\)
2A = \(7\left(\frac{2}{5.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{2015.2017}\right)\)
2A = \(7\left(\frac{1}{5}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{2015}-\frac{1}{2017}\right)\)
2A = \(7\left(\frac{1}{5}-\frac{1}{2017}\right)\)
2A = \(7\cdot\frac{2012}{10085}\)
2A = \(\frac{14084}{10085}\)
A = \(\frac{14084}{10085}:2\)
A = \(\frac{7042}{10085}\)
\(\frac{7}{5.9}+\frac{7}{9.11}+\frac{7}{11.13}+\frac{7}{11.13}+...+\frac{7}{2015.2017}\)
\(=\frac{7}{5.9}+\frac{7}{2}.\left(\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{2015.2017}\right)\)
\(=\frac{7}{45}+\frac{7}{2}.\left(\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{2015}-\frac{1}{2017}\right)\)
\(\frac{x-2}{2}-\frac{1+x}{3}=\frac{4-3x}{4}-1\)
\(\Leftrightarrow\frac{3\left(x-2\right)-2\left(1+x\right)}{6}=\frac{4-3x-4}{4}\)
\(\Leftrightarrow\frac{3x-6-2-2x}{6}=-\frac{3x}{4}\)
\(\Leftrightarrow\frac{x-8}{6}=-\frac{3x}{4}\)
\(\Leftrightarrow4x-32=-18x\)
\(\Rightarrow x=\frac{16}{11}\)
A = 1/2^2 + 1/3^2 + 1/4^2 + ... + 1/100^2
1/2^2 < 1/1*2
1/3^2 < 1/2*3
1/4^2 < 1/3*4
...
1/100^2 < 1/99*100
=> A < 1/1*2 + 1/2*3 + 1/3*4 + ... + 1/99*100
=> A < 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/99 - 1/100
=> A < 1 - 1/100
=> A < 1
minh deo can ban k dau :((
\(a,\frac{1}{2}x+\frac{3}{5}(x-2)=3\)
\(\Rightarrow\frac{1}{2}x+\frac{3}{5}x-\frac{6}{5}=3\)
\(\Rightarrow\left[\frac{1}{2}+\frac{3}{5}\right]x=3+\frac{6}{5}\)
\(\Rightarrow\left[\frac{5}{10}+\frac{6}{10}\right]x=\frac{21}{5}\)
\(\Rightarrow\frac{11}{10}x=\frac{21}{5}\)
\(\Rightarrow x=\frac{21}{5}:\frac{11}{10}=\frac{21}{5}\cdot\frac{10}{11}=\frac{21}{1}\cdot\frac{2}{11}=\frac{42}{11}\)
Vậy x = 42/11
1 + 2 + 3 + 4 + 5 +...+ x = 1540 giúp mk nhé ai nhanh mk tick cho ai trả lời lm ny mk ( nếu là trai)
\(1+2+3+4+5+...+x=1540\)
Ta có :
\(\frac{x\cdot\left(x+1\right)}{2}=1540\)
\(x\cdot\left(x+1\right)=1540\cdot2\)
\(x\cdot\left(x+1\right)=3080\)
Vì \(x\cdot\left(x+1\right)\)là tích của hai số tự nhiên liên tiếp
\(\Rightarrow55\cdot56=3080\)
Vậy \(x=55\)
Ta có: 1+2+3+4+5....+x=1540
=> \(x\times\left(x+1\right):2=1540\)
\(\Rightarrow x\times\left(x+1\right)=3080\)
Vì 55 x 56 = 3080
Nên x = 55
\(\frac{11.3^{29}-\left(3.3\right)^{15}}{2^2.3^{28}}\)=\(\frac{11.3^{29}-3^{30}}{2^2.3^{28}}=\frac{3^{29}.\left(11-3\right)}{3^{28}.2^2}=\frac{3.8}{2^2}=3.2\)=6
các bn lm đến đâu cx dc miễn là lm hộ mk cái ạ, ai đang lm vào nhắn tin vs mk để mk bít nha
a; \(-\dfrac{8}{3}+\dfrac{7}{5}-\dfrac{71}{15}< x< -\dfrac{13}{7}+\dfrac{19}{14}-\dfrac{7}{2}\)
-\(\dfrac{19}{15}\) - \(\dfrac{71}{15}\) < \(x\) < -\(\dfrac{1}{2}\) - \(\dfrac{7}{2}\)
-6 < \(x\) < -4
vì \(x\) \(\in\) Z nên \(x\) = -5
(-\(\frac{4}{12}\)) +7=(\(-\frac{1}{3}\)) + 7
=(-\(\frac{1}{3}\))+\(\frac{21}{3}\)
=\(\frac{20}{3}\)
(- 4 /12 ) + 7 = ( - 1/3 ) + 7= ( - 1/3 ) + 21/3
= 20/3