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a) \(S=\left(-\frac{1}{7}\right)^0+\left(-\frac{1}{7}\right)^1+\left(-\frac{1}{7}\right)^2+...+\left(-\frac{1}{7}\right)^{2007}\)
\(=1+\left(-\frac{1}{7}\right)+\left(-\frac{1}{7}\right)^2+...+\left(-\frac{1}{7}\right)^{2007}\)
=> 7S = \(7+\left(-1\right)+\left(-\frac{1}{7}\right)+...+\left(-\frac{1}{7}\right)^{2006}\)
Lấy 7S trừ S ta có :
7S - S = \(7+\left(-1\right)+\left(-\frac{1}{7}\right)+...+\left(-\frac{1}{7}\right)^{2006}-\left[1+\left(-\frac{1}{7}\right)+\left(-\frac{1}{7}\right)^2+...+\left(-\frac{1}{7}\right)^{2007}\right]\)
6S = \(7-1-1+\left(\frac{1}{7}\right)^{2007}=5+\left(\frac{1}{7}\right)^{2007}\Rightarrow S=\frac{5+\left(\frac{1}{7}\right)^{2007}}{6}\)
a, 7/12 - 3/4 . 5/6
= 7/12 - 5/8
= 14/24- 15/24
= -1/24
b,( 2/1/3 + 1/3/4 ) . 12/13
= ( 6/3 + 7/3 ) . 12/13
= 13/3 . 12/13
=4
c, 12 : ( 3/4 -5/6 ) . 2
= 12 : ( -1/12 ) .2
= 12 . -12 . 2
= -228
d, 7/22 : 3/11 + 7/22 : 4/11
= 7/22 . 11/3 + 7/22 . 11/4
= 7/22 . ( 11/3 + 11/4 )
....
tiếp theo bạn tự làm nhé!
\(a,\left(\frac{3}{8}+-\frac{3}{4}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)
= \(\left(-\frac{3}{8}+\frac{7}{12}\right):\frac{5}{6}+\frac{1}{2}\)
= \(\frac{5}{24}:\frac{5}{6}+\frac{1}{2}\)
= \(\frac{1}{4}+\frac{1}{2}\)
= \(\frac{3}{4}\)
b)\(-\frac{7}{3}.\frac{5}{9}+\frac{4}{9}.\left(-\frac{3}{7}\right)+\frac{17}{7}\)
=\(-\frac{35}{27}+\left(-\frac{4}{21}\right)+\frac{17}{7}\)
= \(-\frac{35}{27}+\frac{47}{21}\)
= \(\frac{178}{189}\)
c) \(\frac{117}{13}-\left(\frac{2}{5}+\frac{57}{13}\right)\)
= \(\frac{117}{13}-\frac{311}{65}\)
= \(\frac{274}{65}\)
d) \(\frac{2}{3}-0,25:\frac{3}{4}+\frac{5}{8}.4\)
= \(\frac{2}{3}-\frac{1}{4}:\frac{3}{4}+\frac{5}{8}.4\)
= \(\frac{2}{3}-\frac{1}{3}+\frac{5}{2}\)
= \(\frac{1}{3}+\frac{5}{2}\)
= \(\frac{17}{6}\)
A = \(\dfrac{1}{2}\) - 0,75 + \(\dfrac{5}{4}\) - \(\dfrac{6}{12}\)
A = 0,5 - 0,75 + 1,25 - 0,5
A = (0,5 - 0,5) + (1,25 - 0,75)
A = 0,5
B = (-\(\dfrac{1}{7}\))0 - 22.(\(\dfrac{2}{3}\))2
B = 1 - 22. \(\dfrac{4}{9}\)
B = 1 - \(\dfrac{88}{9}\)
B = - \(\dfrac{79}{9}\)
\(=\left(3.5-0.5\right)\cdot\dfrac{1}{27}+\dfrac{4}{3}=\dfrac{1}{9}+\dfrac{4}{3}=\dfrac{1}{9}+\dfrac{12}{9}=\dfrac{13}{9}\)
1.Thực hiện phép tính :
a) -4,3y - \(\frac{1}{2}y-\frac{3}{4}=-0,4\)
=> (-4,3- \(\frac{1}{2}\))y = -0,4 + \(\frac{3}{4}\)
=> \(\frac{-24}{5}\)y = \(\frac{7}{20}\)
=> y = \(\frac{7}{20}:\frac{-24}{5}\)
=> y = \(\frac{-7}{96}\)
b) 4\(\left(y-\frac{1}{3}\right)^3=0\)
=> y3 - \(\frac{1}{3}^3\) = 0
=> y3 - \(\frac{1}{27}=0\)
=> y3 = \(\frac{1}{27}\)
=> y = \(\frac{1}{3}\)
c) 13 -2 . | 1 - 2y | = 1
=> 2.| 1 - 2y | = 13 - 1
=> 2.| 1 - 2y | = 12
=> | 1 - 2y | = 6
=> \(\left[\begin{matrix}1-2y=6\\1-2y=-6\end{matrix}\right.\)
=> \(\left[\begin{matrix}2y=-5\\2y=7\end{matrix}\right.\)
=> \(\left[\begin{matrix}y=\frac{-5}{2}\\y=\frac{7}{2}\end{matrix}\right.\)
Bài 1:
a)\(\frac{-4}{3}.y.\frac{-1}{2}.y.\frac{-3}{4}=-0.4\)
\(\Leftrightarrow\frac{-4}{3}.\frac{-3}{4}.\frac{-1}{2}.y^2=\frac{-2}{5}\)
\(\Leftrightarrow\frac{-1}{2}y^2=\frac{-2}{5}\)
\(\Leftrightarrow y^2=\frac{4}{5}\)
\(\Leftrightarrow\left[\begin{matrix}y=\sqrt{\frac{4}{5}}\\y=-\sqrt{\frac{4}{5}}\end{matrix}\right.\)
b) \(4.\left(y-\frac{1}{3}\right)^3=0\)
\(\Leftrightarrow\left(y-\frac{1}{3}\right)^3=0\)
\(\Leftrightarrow y-\frac{1}{3}=0\)
\(\Leftrightarrow y=\frac{1}{3}\)
c) 13-2.|1-2y|=1
<=>2.|2y-1|=12
<=>|2y-1|=6
<=> \(\left[\begin{matrix}2y-1=6\\2y-1=-6\end{matrix}\right.\)
<=>\(\left[\begin{matrix}y=3,5\\y=-2,5\end{matrix}\right.\)