a) Tính tổng: S = (-1/7)0 + (-1/7)1 + (-1/7)2 +...+ (-1/7)2007
b) Thực hiện phép tính: M = 1 + 1/2*(1+2) + 1/3*(1+2+3) + 1/4*(1+2+3+4) +...+ 1/16*(1+2+3+...+16)
K
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Những câu hỏi liên quan
19 tháng 12 2020
a) Ta có: \(\left|5\cdot0.6+\dfrac{2}{3}\right|-\dfrac{1}{3}\)
\(=\left|3+\dfrac{2}{3}\right|-\dfrac{1}{3}\)
\(=3+\dfrac{2}{3}-\dfrac{1}{3}\)
\(=3+\dfrac{1}{3}=\dfrac{10}{3}\)
b) Ta có: \(\left(0.25-1\dfrac{1}{4}\right):5-\dfrac{1}{5}\cdot\left(-3\right)^2\)
\(=\left(\dfrac{1}{4}-\dfrac{5}{4}\right)\cdot\dfrac{1}{5}-\dfrac{1}{5}\cdot9\)
\(=\dfrac{-4}{4}\cdot\dfrac{1}{5}-\dfrac{1}{5}\cdot9\)
\(=\dfrac{1}{5}\cdot\left(-1-9\right)\)
\(=-10\cdot\dfrac{1}{5}=-2\)
c) Ta có: \(\dfrac{14}{17}\cdot\dfrac{7}{5}-\dfrac{-3}{17}:\dfrac{5}{7}\)
\(=\dfrac{14}{17}\cdot\dfrac{7}{5}-\dfrac{-3}{17}\cdot\dfrac{7}{5}\)
\(=\dfrac{7}{5}\cdot\left(\dfrac{14}{17}+\dfrac{3}{17}\right)\)
\(=\dfrac{7}{5}\cdot1=\dfrac{7}{5}\)
d) Ta có: \(\dfrac{7}{16}+\dfrac{-9}{25}+\dfrac{9}{16}+\dfrac{-16}{25}\)
\(=\left(\dfrac{7}{16}+\dfrac{9}{16}\right)-\left(\dfrac{9}{25}+\dfrac{16}{25}\right)\)
\(=\dfrac{16}{16}-\dfrac{25}{25}\)
\(=1-1=0\)
e) Ta có: \(\dfrac{5}{6}+2\sqrt{\dfrac{4}{9}}\)
\(=\dfrac{5}{6}+2\cdot\dfrac{2}{3}\)
\(=\dfrac{5}{6}+\dfrac{4}{3}\)
\(=\dfrac{5}{6}+\dfrac{8}{6}=\dfrac{13}{6}\)
25 tháng 6 2023
`@` `\text {Ans}`
`\downarrow`
`a.`
`A=(1/2-7/13-1/3)+(-6/13+1/2+1 1/3)`
`= 1/2 - 7/13 - 1/3 - 6/13 + 1/2 + 1 1/3`
`= (1/2 + 1/2) + (-7/13 - 6/13) + (-1/3 + 1 1/3) `
`= 1 - 1 + 1`
`= 1`
`b.`
`B=0,75+2/5+(1/9-1 1/2+5/4)`
`= 3/4 + 2/5 + 1/9 - 3/2 + 5/4`
`= (3/4+5/4)+ 1/9 + 2/5 - 3/2`
`= 2 + 1/9 - 11/10`
`= 19/9 - 11/10`
`= 91/90`
`c.`
`(-5/9).3/11+(-13/18).3/11`
`= 3/11*[(-5/9) + (-13/18)]`
`= 3/11*(-23/18)`
`= -23/66`
`d.`
`(-2/3).3/11+(-16/9).3/11`
`= 3/11* [(-2/3) + (-16/9)]`
`= 3/11*(-22/9)`
`= -2/3`
`e.`
`(-1/4).(-2/13)-7/24.(-2/13)`
`= (-2/13)*(-1/4-7/24)`
`= (-2/13)*(-13/24)`
`= 1/12`
`f.`
`(-1/27).3/7+(5/9).(-3/7)`
`= 3/7*(-1/27 - 5/9)`
`= 3/7*(-16/27)`
`= -16/63`
`g.`
`(-1/5+3/7):2/11+(-4/5+4/7):2/11`
`=[(-1/5+3/7)+(-4/5+4/7)] \div 2/11`
`= (-1/5+3/7 - 4/5 + 4/7) \div 2/11`
`= [(-1/5-4/5)+(3/7+4/7)] \div 2/11`
`= (-1+1) \div 2/11`
`= 0 \div 2/11 = 0`
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
15 tháng 12 2023
a, (\(\dfrac{9}{10}\) - \(\dfrac{15}{16}\)) \(\times\) ( \(\dfrac{5}{12}\) - \(\dfrac{11}{15}\) - \(\dfrac{7}{20}\))
= (\(\dfrac{72}{80}\) - \(\dfrac{75}{80}\)) \(\times\) (\(\)\(\dfrac{25}{60}\) - \(\dfrac{44}{60}\) - \(\dfrac{21}{60}\))
= - \(\dfrac{3}{80}\) \(\times\) (- \(\dfrac{2}{3}\))
= \(\dfrac{1}{40}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
15 tháng 12 2023
b, (-1)3 + (- \(\dfrac{2}{3}\))2 : 2\(\dfrac{2}{3}\) + \(\dfrac{5}{6}\)
= -13 + \(\dfrac{4}{9}\) : \(\dfrac{8}{3}\) + \(\dfrac{5}{6}\)
= -1 + \(\dfrac{4}{9}\) \(\times\) \(\dfrac{3}{8}\) + \(\dfrac{5}{6}\)
= -1 + \(\dfrac{1}{6}\) + \(\dfrac{5}{6}\)
= -1 + 1
= 0
25 tháng 6 2023
4:
a: =4/15-2,9+11/15=1-2,9=-1,9
b: \(=-36,75+3,7-63,25+6,3=10-100=-90\)
c: \(=6,5+3,5-\dfrac{10}{17}-\dfrac{7}{17}=10-1=9\)
d: \(=\dfrac{13}{25}\left(-39,1-60,9\right)=\dfrac{13}{25}\left(-100\right)=-52\)
e: =-5/12-7/12-3,7-6,3=-1-10=-11
f: =2,8(-6/13-7/13)-7,2=-2,8-7,2=-10
HL
0
4 tháng 5 2018
1 .
[ 6 + ( 1/2 ) 3 - /-0,5/ ] : 3/12
= [ 6 + 1/8 - ( -5/10 ) ] . 12/3
= [ 6 + 1/8 + 5/10 ] .4
= [ 6 + 1/8 + 1/2 ] .4
= [ 48/8 + 1/8 + 4/8 ] .4
= 53/8 . 4
= 53 . 1/2
= 53/2
2.
1/3 + 5/4 : (-35/16)
= 1/3 + 5/4 . ( 16/-35 )
= 1/3 + 1 . 4/4 . (-7 )
= 1/3 + 4/28
= 1/3 + 1/7
= 7/21 + 3/21
= 10/21
3 .
11 3/13 - ( 2 4/7 + 5 3/13 )
= 11 3/13 - 2 4/7 - 5 3/13
= { [ ( 11 - 5 ) . ( 3/13 - 3/13 ) } - 2 4/7
= ( 6 . 0 ) - 2 4/7
= 0 - 18/7
= 18/7
4 .
1 3/7 + (-1/3 + 2 4/7 )
= 1 3/7 + ( -1 )/3 + 2 4/7
={ [ ( 1 + 2 ) . ( 3/7 + 4/7 ) } + ( -1 )/3
= ( 3 . 1 ) + ( -1 )/3
= 3 + ( -1 )/3
= 9/3 + ( -1 )/3
= 8/3
5 .
( 6 4/9 + 3 7/11 ) - 4 4/9
= 6 4/9 + 3 7/11 - 4 4/9
= { ( 6 - 4 ) . ( 4/9 - 4/9 ) } + 3 7/11
= ( 2 . 0 ) + 3 7/11
= 0 + 40/11
= 40/11
Nếu đúng thì k cho mình nha !
KV
4 tháng 12 2023
a) 1/2 + 3/4 - (3/4 - 4 - 5)
= 1/2 + 3/4 - 3/4 + 4 + 5
= (3/4 - 3/4) + (4 + 5) + 1/2
= 0 + 9 + 1/2
= 19/2
b) [9/16 + 8/(-27)] - (19/27- 7/16 - 2)
= 9/16 - 8/27 - 19/27 + 7/16 + 2
= (9/16 + 7/16) + (-8/27 - 19/27) + 2
= 1 - 1 + 2
= 2
c) -5/8 . [4/9 + 7/(-12)]
= -5/8 . (-5/36)
= 25/288
d) 7/10 . (-3/5) + 7/10 . (-2/5) - (-3/10)
= 7/10 . (-3/5 - 2/5) + 3/10
= 7/10 . (-1) + 3/10
= -2/5
e) -3/7 . 5/9 + 4/9 . (-3/7) + 2 3/7
= -3/7 . (5/9 + 4/9) + 17/7
= -3/7 . 1 + 17/7
= 2
f) 8 2/7 - (3 4/9 + 4 2/7)
= 8 + 2/7 - 3 - 4/9 - 4 - 2/7
= (8 - 3 - 4) + (2/7 - 2/7) - 4/9
= 1 - 4/9
= 5/9
h) 3.(-1/2)² - (4/5 + 8/15) : 5/6
= 3.1/4 - 4/3 : 5/6
= 3/4 - 8/5
= -17/20
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 = \(7-1-1+\left(\frac{1}{7}\right)^{2007}=5+\left(\frac{1}{7}\right)^{2007}\Rightarrow S=\frac{5+\left(\frac{1}{7}\right)^{2007}}{6}\)