\(A=1-2+3-4+5-6+7-8+...+99-100\)

\(A=\left(-1\right)+\left(-1\right)+\left(-1\right)+\left(-1\right)+...+\left(-1\right)\)

\(A=\left(-1\right).50\)

\(A=-50\)

\(B=1+3-5-7+9+11-...-397-399\)

\(B=1-2+2-2+2-...+2-2-399\)

\(B=1-399\)

\(B=-398\)

\(C=1-2-3+4+5-6-7+...+97-98-99+100\)

\(C=-1+1-1+1-...-1+1\)

\(C=0\)

\(D=2^{2024}-2^{2023}-...-1\)

\(D=2^{2024}-\left(2^0+2^1+2^2+...2^{2023}\right)\)

\(D=2^{2024}-\left(\dfrac{2^{2024}-1}{2-1}\right)\)

\(D=2^{2024}-\left(2^{2024}-1\right)\)

\(D=2^{2024}-2^{2024}+1\)

\(D=1\)

A = 1 - 2 + 3  - 4 + 5 - 6 + 7 - 8 +...+ 99 - 100

A = (1 - 2) + ( 3 - 4) + ( 5- 6) +....+(99 - 100)

Xét dãy số 1; 3; 5;...;99

Dãy số trên là dãy số cách đều có khoảng cách là: 3 - 1 = 2

Dãy số trên có số số hạng là: (99 - 1) : 2 + 1 = 50 (số)

Vậy tổng A có 50 nhóm, mỗi nhóm có giá trị là: 1- 2 = -1

A =  - 1\(\times\)50 = -50

b, 

B = 1 + 3 - 5 - 7 + 9 + 11-...- 397 - 399

B = ( 1 + 3 - 5 - 7) + ( 9 + 11 - 13 - 15) + ...+( 393 + 395 - 397 - 399)

B = -8 + (-8) +...+ (-8)

Xét dãy số 1; 9; ...;393

Dãy số trên là dãy số cách đều có khoảng cách là: 9-1 = 8

Dãy số trên có số số hạng là: ( 393 - 1): 8 + 1 = 50 (số hạng)

Tổng B có 50 nhóm mỗi nhóm có giá trị là -8

B = -8 \(\times\) 50 = - 400

c, 

C = 1 - 2 - 3 + 4 + 5 -  6 +...+ 97 - 98 - 99 +100

C = ( 1 - 2 - 3 + 4) + ( 5 - 6 - 7+ 8) +...+ ( 97 - 98 - 99 + 100)

C = 0 + 0 + 0 +...+0

C = 0

d,   D =           2²⁰²⁴ - 2²⁰²³- ... +2 - 1

    2D = 2²⁰⁰⁵- 2²⁰⁰⁴ + 2²⁰⁰³+...- 2

2D + D = 2²⁰⁰⁵ - 1

 3D      = 2²⁰⁰⁵ - 1

   D      = (2²⁰⁰⁵ - 1): 3

T=(a*2/3):5/6 a:8/15 với a=-4/5

I=3/4*a+4/9*a-1/4*a với a=12/5

P=a(b+1/5)-a*(6/5+b) với a= 2004 ;b=206

Q=1/19*a+3*b:5/7+9/4 với a=38;b=-10/7

V=3/2*(a+b+c)- 1/5*(a-b-c) với a=1/3;b=-5/6;c=3/4

giúp mình với

a; 5\(\dfrac{3}{4}\) : 3 + 2\(\dfrac{1}{4}\).\(\dfrac{1}{3}\) - \(\dfrac{3}{8}\)

= \(\dfrac{23}{4}\) : 3 + \(\dfrac{9}{4}\).\(\dfrac{1}{3}\) - \(\dfrac{3}{8}\)

= \(\dfrac{23}{4}\) x \(\dfrac{1}{3}\) + \(\dfrac{3}{4}\) - \(\dfrac{3}{8}\)

= \(\dfrac{23}{12}\) + \(\dfrac{3}{4}\) - \(\dfrac{3}{8}\)

= \(\dfrac{46}{24}\) + \(\dfrac{18}{24}\) - \(\dfrac{9}{24}\)

= \(\dfrac{64}{24}\) - \(\dfrac{9}{24}\)

= \(\dfrac{55}{24}\)

a) \(\dfrac{13}{20}+\dfrac{3}{5}+x=\dfrac{5}{6}\)

\(\Rightarrow\dfrac{5}{4}+x=\dfrac{5}{6}\)

\(\Rightarrow x=\dfrac{5}{6}-\dfrac{5}{4}\)

\(\Rightarrow x=\dfrac{-5}{12}\)

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

\(\Rightarrow x+\dfrac{1}{3}=\dfrac{11}{15}\)

\(\Rightarrow x=\dfrac{11}{15}-\dfrac{1}{3}\)

\(\Rightarrow x=\dfrac{2}{5}\)

c)\(\dfrac{-5}{8}-x=\dfrac{-3}{20}-\dfrac{-1}{6}\)

\(\dfrac{-5}{8}-x=\dfrac{1}{60}\)

\(\Rightarrow x=\dfrac{-5}{8}-\dfrac{1}{60}\)

\(\Rightarrow x=\dfrac{-77}{120}\)

d) \(\dfrac{3}{5}-x=\dfrac{1}{4}+\dfrac{7}{10}\)

\(\Rightarrow\dfrac{3}{5}-x=\dfrac{19}{20}\)

\(\Rightarrow x=\dfrac{3}{5}-\dfrac{19}{20}\)

\(\Rightarrow x=\dfrac{-7}{20}\)

e) \(\dfrac{-3}{7}-x=\dfrac{4}{5}+\dfrac{-2}{3}\)

\(\Rightarrow\dfrac{-3}{7}-x=\dfrac{2}{15}\)

\(\Rightarrow x=\dfrac{-3}{7}-\dfrac{2}{15}\)

\(\Rightarrow x=\dfrac{-59}{105}\)

g) \(\dfrac{-5}{6}-x=\dfrac{7}{12}+\dfrac{-1}{3}\)

\(\Rightarrow\dfrac{-5}{6}-x=\dfrac{1}{4}\)

\(\Rightarrow x=\dfrac{-5}{6}-\dfrac{1}{4}\)

\(\Rightarrow x=\dfrac{-13}{12}\)

bạn ghi + - x : nhá

a) \(\dfrac{-5}{11}+\left(\dfrac{-6}{11}+1\right)\)

\(=\dfrac{-5}{11}+\left(\dfrac{-6}{11}+\dfrac{11}{11}\right)\)

\(=\dfrac{-5}{11}+\dfrac{5}{11}\)

\(=0\)

b) \(\dfrac{2}{3}+\left(\dfrac{5}{7}+\dfrac{-2}{3}\right)\)

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

\(=0+\dfrac{5}{7}\)

\(=\dfrac{5}{7}\)

c) \(\left(\dfrac{-1}{4}+\dfrac{5}{8}\right)+\dfrac{-3}{8}\)

\(=\dfrac{-1}{4}+\dfrac{-3}{8}+\dfrac{5}{8}\)

\(=\dfrac{-2}{8}+\dfrac{-3}{8}+\dfrac{5}{8}\)

\(=0\)

d) \(\dfrac{3}{4}.\dfrac{7}{25}+\dfrac{3}{4}.\dfrac{18}{25}\)

\(=\dfrac{3}{4}.\left(\dfrac{7}{25}+\dfrac{18}{25}\right)\)

\(=\dfrac{3}{4}.1\)

\(=\dfrac{3}{4}\)

Chúc bạn học tốt

=17/6:(1-2/3)

=17/6:1/3

=17/2

=13/6×9/2-6/7

=39/4-6/7

=249/28

a) \(\left(\frac{5}{2}+\frac{1}{3}\right):\left(1-\frac{2}{3}\right)=\left(\frac{15}{6}+\frac{2}{6}\right):\frac{1}{3}\)

\(=\frac{17}{6}:\frac{1}{3}=\frac{17}{6}\cdot\frac{3}{1}=\frac{17}{2}\cdot\frac{1}{1}=\frac{17}{2}\)

b) \(\left(\frac{5}{2}-\frac{1}{3}\right)\cdot\frac{9}{2}-\frac{6}{7}=\left(\frac{15}{6}-\frac{2}{6}\right)\cdot\frac{9}{2}-\frac{6}{7}\)

\(=\frac{13}{6}\cdot\frac{9}{2}-\frac{6}{7}=\frac{13}{2}\cdot\frac{3}{2}-\frac{6}{7}=\frac{39}{4}-\frac{6}{7}=\frac{273}{28}-\frac{24}{28}=\frac{249}{28}\)

a ) \(\left(\frac{5}{2}+\frac{1}{3}\right)\div\left(1-\frac{2}{3}\right)\)

\(=\left(\frac{15}{6}+\frac{2}{6}\right)\div\frac{1}{3}\)

\(=\frac{17}{6}\div\frac{1}{3}=\frac{17}{6}\cdot\frac{3}{1}\)

\(=\frac{17}{2}\)

b ) \(\left(\frac{5}{2}-\frac{1}{3}\right)\cdot\frac{9}{2}-\frac{6}{7}\)

\(=\left(\frac{15}{6}-\frac{2}{6}\right)\cdot\frac{9}{2}-\frac{6}{7}\)

\(=\frac{13}{6}\cdot\frac{51}{14}\)

\(=\frac{221}{28}\)

a)(-0,25).4/17.(-3 5/21).(-7/12)

= -1/17 . (-68/21) . ( -7/21)

= -4/63

b) (-2/5).4/15+(-3/10).4/15

= 4/15. [-2/5 + (-3/10)]

= 4/15 . (-7/10)

= -14/75

c)21-3 3/4:(3/8-1/6)

= 21 - 15/4 : 5/24

= 21 - 18

= 3

d) (-3/4+2/5):3/7+(3/5+-1/4):3/7

= [(-3/4 + 2/5) + (3/5 + -1/4)] : 3/7

= [-7/20 + (-17/20)] : 3/7

= -6/5 : 3/7

= -14/5

a) \(...=-\dfrac{1}{4}.\dfrac{4}{17}.\left(-\dfrac{63}{21}\right).\left(-\dfrac{7}{12}\right)\)

\(=-\dfrac{1}{17}.\dfrac{63}{21}.\dfrac{7}{12}\)

\(=-\dfrac{7}{68}\)

b) \(...=-\dfrac{2}{5}.\dfrac{4}{15}-\dfrac{3}{10}.\dfrac{4}{15}\)

\(=\dfrac{4}{15}\left(-\dfrac{2}{5}-\dfrac{3}{10}\right)\)

\(=\dfrac{4}{15}\left(-\dfrac{4}{10}-\dfrac{3}{10}\right)\)

\(=\dfrac{4}{15}.\left(-\dfrac{7}{10}\right)=-\dfrac{14}{75}\)

c) \(...=21-\dfrac{15}{4}:\left(\dfrac{9}{24}-\dfrac{4}{24}\right)\)

\(=21-\dfrac{15}{4}:\dfrac{5}{24}\)

\(=21-\dfrac{15}{4}.\dfrac{24}{5}\)

\(=21-3.6=3\)

d) \(...=\left(-\dfrac{3}{4}+\dfrac{2}{5}\right).\dfrac{7}{3}+\left(\dfrac{3}{5}-\dfrac{1}{4}\right).\dfrac{7}{3}\)

\(=\dfrac{7}{3}\left(-\dfrac{3}{4}+\dfrac{2}{5}+\dfrac{3}{5}-\dfrac{1}{4}\right)\)

\(=\dfrac{7}{3}\left(-\dfrac{3}{4}-\dfrac{1}{4}+\dfrac{2}{5}+\dfrac{3}{5}\right)\)

\(=\dfrac{7}{3}\left(-1+1\right)=0\)