A= 2001000

B= 10100

C= 62500

\(A=1+2+3+4+5+...+2000\)

Số phần tử trong dãy: \(\dfrac{2000-1}{1}+1=2000\)

Tổng của dãy trên: \(A=(2000+1)\cdot2000:2=2001000\)

\(B=2+4+6+8+10+...+200\)

Số phần tử trong dãy: \(\dfrac{200-2}{2}+1=100\)

Tổng của dãy trên: \(B=(200+2)\cdot100:2=10100\)

\(C=1+3+5+7+9+...+499\)

Số phần tử trong dãy: \(\dfrac{499-1}{2}+1=250\)

Tổng của dãy trên: \(C=(499+1)\cdot250:2=62500\)

tổng A có số số hạng là: A= (2000 - 1) : 1 +1 = 2000 (số hạng)

tổng A là : A = (2000 + 1) x 2000 : 2= 2001000 

tổng B có số số hạng là: B = (200 - 2) : 2 + 1 = 100 (số hạng)

tổng B là: B = (200 + 2) x 100 : 2 = 10100

tổng C có số số hạng là: (499 - 1) : 2 + 1 = 250 (số hạng)

tổng C là: C = (499 + 1) x 250 : 2 = 62500

Câu hỏi

a)3/4 x 2/9 + 1/3

=1/6 + 1/3

=1/6 + 2/6

=1/2

b)5/4:2.9+1/2 

=1.25 : 2.9 + 1/2

=25/58 + 1/2 =27/29

c)7/2 - 1/4 x 1/5

=7/2 - 1/20

=69/20

d)5/4+1/5:2/3

=5/4 + 3/10

=31/20

Học tốt!

câu hỏi là tính

a\()\) 16/9 +3/5

=107/45

b\()\) 4/13--2/17

=51/221--26/221

=77/221

c\()\) -3/2+4/5

=-15/10+8/10

=-7/10

d\()\) 3/-4-1/4

=-1

e\()\) -1/5.5/7

=-1/7

f\()\) 7/8.64/49

=8/7

g\()\) 3/4.15/24

=15/32

a) \(\dfrac{1}{2}-\left(x+\dfrac{1}{3}\right)=\dfrac{5}{6}\)

\(\Rightarrow x+\dfrac{1}{3}=\dfrac{1}{2}-\dfrac{5}{6}\)

\(\Rightarrow x+\dfrac{1}{3}=\dfrac{-1}{3}\)

\(\Rightarrow x=\dfrac{-1}{3}-\dfrac{1}{3}\)

\(\Rightarrow x=\dfrac{-2}{3}\)

b)\(\dfrac{3}{4}-\left(x+\dfrac{1}{2}\right)=\dfrac{4}{5}\)

\(\Rightarrow x+\dfrac{1}{2}=\dfrac{3}{4}-\dfrac{4}{5}\)

\(\Rightarrow x+\dfrac{1}{2}=\dfrac{-1}{20}\)

\(\Rightarrow x=\dfrac{-1}{20}-\dfrac{1}{2}\)

\(\Rightarrow x=\dfrac{-11}{20}\)

c) \(\dfrac{3}{35}-\left(\dfrac{3}{5}+x\right)=\dfrac{2}{7}\)

\(\Rightarrow\dfrac{3}{5}+x=\dfrac{3}{35}-\dfrac{2}{7}\)

\(\Rightarrow\dfrac{3}{5}+x=\dfrac{-1}{5}\)

\(\Rightarrow x=\dfrac{-1}{5}-\dfrac{3}{5}\)

\(\Rightarrow x=\dfrac{-4}{5}\)

d)\(\dfrac{2}{3}.x=\dfrac{4}{27}\)

\(\Rightarrow x=\dfrac{4}{27}:\dfrac{2}{3}\)

\(\Rightarrow x=\dfrac{2}{9}\)

e) \(\dfrac{-3}{5}.x=\dfrac{21}{10}\)

\(\Rightarrow x=\dfrac{21}{10}:\dfrac{-3}{5}\)

\(\Rightarrow x=\dfrac{-7}{2}\)

1)

\(\dfrac{6}{7}+\dfrac{5}{8}:5-\dfrac{3}{16}\cdot\left(-2\right)^2\\ =\dfrac{6}{7}+\dfrac{5}{8}\cdot\dfrac{1}{5}-\dfrac{3}{16}\cdot4\\ =\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{4}\\ =\dfrac{55}{16}-\dfrac{3}{4}\\ =\dfrac{13}{56}\)

2)

\(-\dfrac{1}{6}+\dfrac{2}{3}\cdot\dfrac{-3}{4}+\dfrac{\left(-2\right)^2}{5}\\ =-\dfrac{1}{6}-\dfrac{1}{2}+\dfrac{4}{5}\\ =-\dfrac{2}{3}+\dfrac{4}{5}\\ =\dfrac{2}{15}\)

3)

\(2\dfrac{3}{4}\cdot\left(-0,4\right)+1\dfrac{3}{5}\cdot1,75+\left(-7,2\right):\dfrac{9}{11}\)

\(=\dfrac{11}{4}\cdot\dfrac{-2}{5}+\dfrac{8}{5}\cdot\dfrac{7}{4}-\dfrac{36}{5}\cdot\dfrac{11}{9}\\ =-\dfrac{11}{10}+\dfrac{14}{5}-\dfrac{44}{5}\\ =-\dfrac{11}{10}-6\\ =-\dfrac{71}{10}\)

4)

\(\dfrac{1}{8}\cdot15\dfrac{2}{5}+1\dfrac{4}{5}\cdot\dfrac{7}{8}-17\dfrac{1}{5}\cdot\dfrac{1}{8}\)

\(=\dfrac{1}{8}\cdot\dfrac{77}{5}+\dfrac{9}{5}\cdot\dfrac{7}{8}-\dfrac{86}{5}\cdot\dfrac{1}{8}\)

\(=\dfrac{1}{8}\cdot\dfrac{77}{5}+\dfrac{63}{5}\cdot\dfrac{1}{8}-\dfrac{86}{5}\cdot\dfrac{1}{8}\)

\(=\dfrac{1}{8}\left(\dfrac{77}{5}+\dfrac{63}{5}-\dfrac{86}{5}\right)\\ =\dfrac{1}{8}\cdot\dfrac{54}{5}\\ =\dfrac{27}{20}\)

Bài 1 :

a, \(\frac{3}{4}:x=\frac{5}{12}\)

\(x=\frac{3}{4}:\frac{5}{12}\)

\(x=\frac{9}{5}\)

b, \(x-\frac{1}{2}=\frac{3}{4}:\frac{3}{2}\)

\(x-\frac{1}{2}=\frac{1}{2}\)

\(x=\frac{1}{2}+\frac{1}{2}\)

\(x=1\)

c, \(1\frac{1}{2}x-\frac{1}{2}=\frac{3}{4}\)

\(\frac{3}{2}x-\frac{1}{2}=\frac{3}{4}\)

\(\frac{3}{2}x=\frac{3}{4}+\frac{1}{2}\)

\(\frac{3}{2}x=\frac{5}{4}\)

\(x=\frac{5}{4}:\frac{3}{2}\)

\(x=\frac{5}{6}\)

Bài 2 :

\(A=\frac{-3}{5}+\left(\frac{-2}{5}-99\right)\)

\(A=\frac{-3}{5}+\frac{-2}{5}-99\)

\(A=\left(-1\right)-99\)

\(A=-100\)

\(B=\left(7\frac{2}{3}+2\frac{3}{5}\right)-6\frac{2}{3}\)

\(B=\left(\frac{23}{3}+\frac{13}{5}\right)-\frac{20}{3}\)

\(B=\frac{23}{3}+\frac{13}{5}-\frac{20}{3}\)

\(B=\left(\frac{23}{3}-\frac{20}{3}\right)+\frac{13}{5}\)

\(B=1+\frac{13}{5}\)

\(B=\frac{18}{5}\)

a, 3/4 : x = 5/12

=>        x = 3/4 : 5/12

=>        x = 9/5

Vậy x=9/5

b, x - 1/2 = 3/4 : 3/2

=>x - 1/2 = 1/2

=>x         = 1/2 + 1/2

=>x         = 2/2 = 1

Vậy x = 1

c, 11/2 . x - 1/2 = 3/4

=>11/2 . x         = 3/4 + 1/2

=> 11/2 . x        = 5/4

=>         x          = 5/4 : 11/2

=>          x         = 5/22

Vậy x = 5/22

Bài 2 :

A = -3/5 + ( -2/5 - 99 )

   = -3/5  +  -497/5

   =  -500/5

   =  -100

Vậy A = -100

B = ( 72/3 + 23/5 ) - 62/3

   =  429/15    - 62/3

   =       119/15

Vậy B = 119/15

a, \(\left(5x-10\right)\left(6x-\frac{1}{3}\right)=0\\ \Rightarrow\left[{}\begin{matrix}5x-10=0\\6x-\frac{1}{3}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}5x=10\\6x=\frac{1}{3}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=2\\x=\frac{1}{18}\end{matrix}\right.\)

Vậy \(x\in\left\{2;\frac{1}{18}\right\}\)

b, \(\frac{-3}{4}-\left|\frac{4}{5}-x\right|=-10\\ \frac{-3}{4}+10=\left|\frac{4}{5}-x\right|\\ \left|\frac{4}{5}-x\right|=\frac{37}{4}\\ \Rightarrow\left[{}\begin{matrix}\frac{4}{5}-x=\frac{37}{4}\\\frac{4}{5}-x=\frac{-37}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{4}{5}-\frac{37}{4}\\x=\frac{4}{5}-\frac{-37}{4}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{-169}{20}\\x=\frac{201}{20}\end{matrix}\right.\)

Vậy \(x\in\left\{\frac{-169}{20};\frac{201}{20}\right\}\)

c, \(\left|5+x\right|-\frac{-2}{3}=3\\ \left|5+x\right|=3+\frac{-2}{3}\\ \left|5+x\right|=\frac{7}{3}\\ \Rightarrow\left[{}\begin{matrix}5+x=\frac{7}{3}\\5+x=\frac{-7}{3}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{7}{3}-5\\x=\frac{-7}{3}-5\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{-8}{3}\\x=\frac{-22}{3}\end{matrix}\right.\)

Vậy \(x\in\left\{\frac{-8}{3};\frac{-22}{3}\right\}\)

d, Xem lại đề nhé vì không xuất hiện x thì đẳng thức sai.

a, [ (- 1) . 3 ] + (- 4) - (7.0) + 1

= [- 3 + ( - 4 )] - 0 + 1

= - 7 - 0 + 1

= - 6

b, (-1).(-2)+(-3).(-4)-(-2).(-3)

= [(-1).(-2)] + [(-3).(-4)] - [(-2).(-3)]

= 2 + 12 - 6

= 8

c, (-1).(-2).(-3).(-4).(-5):[(-3)-(-5)]

= (-1).(-2).(-3).(-4).(-5) : 2

= - 120 : 2

= - 60

Chắc chắn đấy!

a, (-1).3+(-4)-7.0+1=-3-4-0+1=-6

b, (-1).(-2)+(-3).(-4)-(-2).(-3)=2+12-6=8

c, (-1).(-2).(-3).(-4).(-5):[(-3)-(-5)]=(-120):2=-60

a, (-1).3+(-4)-7.0+1=-3-4-0+1=-6

b, (-1).(-2)+(-3).(-4)-(-2).(-3)=2+12-6=8

c, (-1).(-2).(-3).(-4).(-5):[(-3)-(-5)]=-120:2=-60