3 2/5 * 2 1/7 ; 8 1/6 : 2 1/2
giúp mk nha mà nhớ các số cách phân số là hỗn số nha
5) (3-1/4+2/3) - (5-1/3-6/5) - (6-7/4+3/2) 6) (6-2/3+1/2) - (5+5/3-3/2)-(3-7/3+5/2)
7) (5/3-3/7+9)-(2+5/7-2/3)+(8/7-4/3-10) 8) (8-9/4+2/7)-(-6-3/7+5/4)-(3+2/4-9/7 pls help me
5: \(=3-\dfrac{1}{4}+\dfrac{2}{3}-5+\dfrac{1}{3}+\dfrac{6}{5}-6+\dfrac{7}{4}-\dfrac{3}{2}\)
\(=3-5-6+\dfrac{-1}{4}+\dfrac{7}{4}+\dfrac{2}{3}+\dfrac{1}{3}+\dfrac{6}{5}-\dfrac{3}{2}\)
\(=-8+\dfrac{3}{2}+1+\dfrac{-3}{10}\)
\(=-7+\dfrac{15-3}{10}=-7+\dfrac{6}{5}=-\dfrac{29}{5}\)
6: \(=6-\dfrac{2}{3}+\dfrac{1}{2}-5-\dfrac{5}{3}+\dfrac{3}{2}-3+\dfrac{7}{3}-\dfrac{5}{2}\)
\(=6-5-3-\dfrac{2}{3}-\dfrac{5}{3}+\dfrac{7}{3}+\dfrac{1}{2}+\dfrac{3}{2}-\dfrac{5}{2}\)
\(=-2-\dfrac{1}{2}=-\dfrac{5}{2}\)
7: \(=\dfrac{5}{3}-\dfrac{3}{7}+9-2-\dfrac{5}{7}+\dfrac{2}{3}+\dfrac{8}{7}-\dfrac{4}{3}-10\)
\(=9-2-10+\dfrac{5}{3}+\dfrac{2}{3}-\dfrac{4}{3}+\dfrac{-3}{7}-\dfrac{5}{7}+\dfrac{8}{7}\)
=-3+1
=-2
8: \(=8-\dfrac{9}{4}+\dfrac{2}{7}+6+\dfrac{3}{7}-\dfrac{5}{4}-3-\dfrac{2}{4}+\dfrac{9}{7}\)
\(=8+6-3+\dfrac{2}{7}+\dfrac{3}{7}+\dfrac{9}{7}-1-\dfrac{2}{4}\)
\(=11+2-1-\dfrac{1}{2}\)
=11+1/2
=11,5
(3-1/4+2/3) - (5-1/3-6/5) - (6-7/4+3/2) (6-2/3+1/2) - (5+5/3-3/2)-(3-7/3+5/2)
(5/3-3/7+9)-(2+5/7-2/3)+(8/7-4/3-10) (8-9/4+2/7)-(-6-3/7+5/4)-(3+2/4-9/7 )
mọi người ơi giúp mik với ạ
a)-1/24-[1/4-(1/2-7/8)]
b)(5/7-7/5)-[-1/2-(-2/7-1/10)
c)(-1/2)-(-3/5)+(-1/9)+1/71-(-2/7)+4/35-7/18
d) (3-1/4+2/3) -(5-1/3-6/5)-(6-7/4+3/2)
a) -1/24 - [ 1/4 - ( 1/2 - 7/8 )]
= -1/24 - [ 1/4 +3/8 ]
= -1/24 - 5/8
= -2/3.
a) -1/24 - [ 1/4 - ( 1/2 - 7/8 )]
= -1/24 - [ 1/4 +3/8 ]
= -1/24 - 5/8
= -2/3.
Xin lỗi nha chỉ có thời gian làm câu a) thôi
a,1/1*2+1/2*3+1/3*4+1/4*5+......+1/9*10
b,2/1*3+2/3*5+2/5*7+2/7*9+2/9*11
c,3/1*3+3/3*5+3/5*7+3/7*9+3/9*11
d,5/1*3+5/3*5+5/5*7+5/7*9+5/9*11
Giúp mình với
a)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\)
= \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{3}{4}+...+\frac{1}{9}-\frac{1}{10}\)
= \(1+\left(\frac{-1}{2}+\frac{1}{2}\right)+\left(\frac{-1}{3}+\frac{1}{3}\right)+...+\left(\frac{-1}{9}+\frac{1}{9}\right)-\frac{1}{10}\)
= \(1-\frac{1}{10}\)
=\(\frac{9}{10}\)
b)\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)
= \(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)
=\(1+\left(\frac{-1}{3}+\frac{1}{3}\right)+\left(\frac{-1}{5}+\frac{1}{5}\right)+\left(\frac{-1}{7}+\frac{1}{7}\right)+\left(\frac{-1}{9}+\frac{1}{9}\right)-\frac{1}{11}\)
=\(1-\frac{1}{11}\)
= \(\frac{10}{11}\)
c) đặt A=\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}\)
\(\frac{1}{3}A\)=\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)
\(\frac{2}{3}A\)=\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)
\(\frac{2}{3}A\)=\(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)
\(\frac{2}{3}A\)=\(1+\left(\frac{-1}{3}+\frac{1}{3}\right)+\left(\frac{-1}{5}+\frac{1}{5}\right)+\left(\frac{-1}{7}+\frac{1}{7}\right)+\left(\frac{-1}{9}+\frac{1}{9}\right)-\frac{1}{11}\)
\(\frac{2}{3}A\)=\(\frac{10}{11}\)
A= \(\frac{10}{11}:\frac{2}{3}\)
A= \(\frac{10}{11}.\frac{3}{2}\)=\(\frac{15}{11}\)
d) giả tương tự câu c kết quả \(\frac{25}{11}\)
tổng đặc biệt đó bạn
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{9\times10}\)
\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\)
\(1-\frac{1}{10}=\frac{9}{10}\)
những câu sau cũng áp dụng như vậy nhé
\(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{9}-\frac{1}{11}\)
\(=1-\frac{1}{11}=\frac{10}{11}\)
\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}\)
\(=\frac{3}{2}.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{9}-\frac{1}{11}\right)\)
\(=\frac{3}{2}.\left(1-\frac{1}{11}\right)=\frac{3}{2}.\frac{10}{11}=\frac{15}{11}\)
(5/7-7/7)-[0,2-(-2/7-1/10]
(3-1/4+2/3)-(5-1/3-5/6)-(6-7/4+-3/2)
1/3-3/4--3/5+1/64-2/9-1/3+1/15
3/5:(1/15-1/6)+3/5:(-1/3-16/15)
1/2(-3/4-13/14):5/7-(-2/21+1/7):7/7
\(\left(\dfrac{5}{7}-\dfrac{7}{7}\right)-\left[0,2-\left(-\dfrac{2}{7}-\dfrac{1}{10}\right)\right]\)
=\(-\dfrac{2}{7}-\left[\dfrac{1}{5}+\dfrac{2}{7}+\dfrac{1}{10}\right]\)
=\(-\dfrac{2}{7}-\dfrac{1}{5}-\dfrac{2}{7}-\dfrac{1}{10}\)
=\(\left(-\dfrac{2}{7}-\dfrac{2}{7}\right)-\left(\dfrac{1}{5}+\dfrac{1}{10}\right)\)
=\(-\dfrac{4}{7}-\left(\dfrac{2}{10}+\dfrac{1}{10}\right)\)
=\(-\dfrac{4}{7}-\dfrac{3}{10}\)
=\(-\dfrac{40}{70}-\dfrac{21}{70}\)
=\(-\dfrac{61}{70}\)
(3 - \(\dfrac{1}{4}\) + \(\dfrac{2}{3}\)) - (5 - \(\dfrac{1}{3}\) - \(\dfrac{5}{6}\)) - (6 - \(\dfrac{7}{4}\) - \(\dfrac{3}{2}\))
= 3 - \(\dfrac{1}{4}\) + \(\dfrac{2}{3}\) - 5 + \(\dfrac{1}{3}\) + \(\dfrac{5}{6}\) - 6 + \(\dfrac{7}{4}\) + \(\dfrac{3}{2}\)
= (3 - 5 - 6) + ( \(\dfrac{7}{4}\) - \(\dfrac{1}{4}\)) + (\(\dfrac{2}{3}\) + \(\dfrac{1}{3}\)) + \(\dfrac{3}{2}\) + \(\dfrac{5}{6}\)
= - 8 + \(\dfrac{3}{2}\) + 1 + \(\dfrac{3}{2}\) + \(\dfrac{5}{6}\)
= (- 8 + 1) + (\(\dfrac{3}{2}\) + \(\dfrac{3}{2}\)) + \(\dfrac{5}{6}\)
= -7 + 3 + \(\dfrac{5}{6}\)
= - 4 + \(\dfrac{5}{6}\)
= \(\dfrac{-19}{6}\)
1, ( -2/5 + 3/10 ) : ( 2/-5 + |-4/3 - 2| )
2, 12,5 . -5/7 + 9 3/4 - 1,5 . 5/7
3, -1/4 . -5/13 - 5/4 . -7/13 + 1/1,3
4, ( -3/4 + 5/13 ) : 2/7 - ( 2 1/4 + 8/13 ) : 2/7
5, ( 3 - 3/4 + 2/3 ) - ( 2 - 4/3 - 3/2 ) - ( 1 - 7/3 - 9/2 )
6, -1/3 - 8/35 + -2/9 - 1/135 z+ 4/5 + -4/9 + 3/7
thang nay rot vl
1; = ( -4/10 + 3/10 ) : ( -2/5 + 2/3 ) = -1/10 : ( -6/15 + 10/15 ) = -1/10 : 4/15 = -1/10 . 15/4 = -15/40 = -3/8
2; = 25/2 . -5/7 + 39/4 + -3/2 . 5/7 = -125/14 + 39/4 + -15/14 = ( -125/14 + -15/14 ) + 39/4 = -10 + 39/4 = -40/4 + 39/4 = -1/4
3; = 5/52 + 35/52 + 40/52 = 40/52 + 40/52 = 80/52 = 20/13
4; = ( -39/52 + 20/52 ) . 7/2 - ( 117/52 + 32/52 ) . 7/2 = -19/52 . 7/2 - 149/52 . 7/2 = ( -19/52 + -149/52 ) . 7/2 = -168/52 .7/2 = -147/13
5; = ( 36/12 + -9/12 + 8/12 ) - ( -12/6 + -8/6 + -9/6 ) - ( 6/6 - 14/6 - 27/6 ) = 35/12 + 10/12 + 70/12 = 115/12
6; = -1/3 + -8/35 +-2/9 + -1/135 +4/5 +-4/9 +3/7 = (-1/3 + -2/9 + -4/9 ) + ( -8/35 + 4/5 + 3/7 ) + -1/135 = ( -1/3 + -2/3 ) + ( -8/35 + 28/35 + 15/35 ) + -1/135 = -1 + 1 + -1/135 = -1/135
tui thay ban Huy dot do
1, ( -2/5 + 3/10 ) : ( 2/-5 + |-4/3 - 2| )
2, 12,5 . -5/7 + 9 3/4 - 1,5 . 5/7
3, -1/4 . -5/13 - 5/4 . -7/13 + 1/1,3
4, ( -3/4 + 5/13 ) : 2/7 - ( 2 1/4 + 8/13 ) : 2/7
5, ( 3 - 3/4 + 2/3 ) - ( 2 - 4/3 - 3/2 ) - ( 1 - 7/3 - 9/2 )
6, -1/3 - 8/35 + -2/9 - 1/135 z+ 4/5 + -4/9 + 3/7
tính các tổng sau
1) A = 1+7+7^2+7^3+....+7^2007
2) B= 1+4 +4^2+4^3+....+4^100
3) C= 1+3^2 +3^4 +3^6+3^8+....+3^100
4) D= 7+7^3 + 7^5+7^7+7^9+....+7^99
5)E= 2+2^3+2^5+2^7+2^9+....+2^2009
6) B = 1+2^2+2^4+2^6+2^8+....+2^200
7) C= 5+5^3+5^5+5^9+....+5^101
8) D = 13+13^3+13^5+...+13^99
Mình làm mẫu 1 bài rùi bạn tự giải những bài còn lại nha
1, 7A = 7+7^2+7^3+....+7^2008
6A = 7A - A = (7+7^2+7^3+....+7^2008)-(1+7+7^2+....+7^2007) = 7^2008-1
=> A = (7^2008-1)/6
Tk mk nha
\(A=1+7+7^2+7^3+...+7^{2007}\)
\(\Rightarrow7A=7+7^2+7^3+7^4+...+7^{2008}\)
\(\Rightarrow7A-A=\left(7+7^2+7^3+...+7^{2008}\right)-\left(1+7+7^2+...+7^{2007}\right)\)
\(\Rightarrow6A=7^{2008}-1\)
\(\Rightarrow A=\frac{7^{2008}-1}{6}\)
4b=4+4^2+4^3+...+4^101
4b-b=(4+4^2+...+4^101)-(1+4+4^2+...+4^100)
3b=4^101-1
b=(4^101-1):3
Trục căn thức ở mẫu.
1) 5/√5 ; 3/2√3 ; 5/√7 ; 2√3/5√7 ; 5/2√3
2) 1/√3 ; 2/√3 + 1 ; 3/√5 - 1 ; 12/√5 - √3 ; 4√3 - 2/7 × √2
1)
\(\dfrac{5}{\sqrt{5}}=\dfrac{5\sqrt{5}}{5}\sqrt{5}\)
\(\dfrac{3}{2\sqrt{3}}=\dfrac{3\sqrt{3}}{2\sqrt{3}}=\sqrt{\dfrac{3}{2}}\)
\(\dfrac{5}{\sqrt{7}}=\dfrac{5\sqrt{7}}{\sqrt{49}}=\left(\dfrac{5}{7}\right)\sqrt{7}\)
1:
\(\dfrac{2\sqrt{3}}{5\sqrt{7}}=\dfrac{2\sqrt{21}}{35}\)
\(\dfrac{5}{2\sqrt{3}}=\dfrac{5\sqrt{3}}{6}\)
2: \(\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{3}}{3}\)
\(\dfrac{2}{\sqrt{3}+1}=\sqrt{3}-1\)
\(\dfrac{3}{\sqrt{5}-1}=\dfrac{3+3\sqrt{5}}{4}\)
\(\dfrac{12}{\sqrt{5}-\sqrt{3}}=6\left(\sqrt{5}+\sqrt{3}\right)=6\sqrt{5}+6\sqrt{3}\)