1-3-5+7+9-11-13+15+...+2017-2019-2021+2023=

=(1-3-5+7)+(9-11-13+15)+...+(2017-2019-2021+2023)=
=0+0+.....+0=0

=2019

= 0

\(\frac{-7}{9}\cdot\frac{4}{11}+\frac{-7}{9}\cdot\frac{7}{11}+5\frac{7}{9}\)

\(=\frac{-7}{9}\cdot\left[\frac{4}{11}+\frac{7}{11}\right]+5\frac{7}{9}\)

\(=\frac{-7}{9}\cdot1+5+\frac{7}{9}\)

\(=\frac{-7}{9}+5+\frac{7}{9}=\frac{-7}{9}+\frac{7}{9}+5=5\)

\(\frac{-7}{9}.\frac{4}{11}+\frac{-7}{9}+\frac{7}{11}+5\frac{7}{9}\)

\(=\frac{-7}{9}.\left(\frac{4}{11}+\frac{7}{11}\right)+\frac{52}{9}\)

\(=\frac{-7}{9}.1+\frac{52}{9}\)

\(=\frac{-7}{9}+\frac{52}{9}\)

\(=\frac{45}{9}=5\)

-7/9 . 4/11 + (-7/9) . 7/11+ 5 . 7/9= -7/9 .( 4/11+ 7/11)+(-5) .(- 7/9)

                                               = -7/9 . 1 +(-5) . (-7/9)

                                               = -7/9.(1 + -5)

                                               = -7/9 . (-4)

                                               =28/4

Lời giải:

$A=(-1-2+3+4)+(-5-6+7+8)+(-9-10+11+12)+...+(-2021-2022+2023+2024)-2024$

$=\underbrace{4+4+...+4}_{506}-2024$
$=4.506-2024=0$

\(\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{5}{7}-\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{11}{13}+\dfrac{13}{15}+\dfrac{11}{13}-\dfrac{9}{11}+\dfrac{7}{9}-\dfrac{5}{7}+\dfrac{3}{5}-\dfrac{1}{3}\)
\(=\left(\dfrac{1}{3}-\dfrac{1}{3}\right)-\left(\dfrac{3}{5}-\dfrac{3}{5}\right)+\left(\dfrac{5}{7}-\dfrac{5}{7}\right)-\left(\dfrac{7}{9}-\dfrac{7}{9}\right)+\left(\dfrac{9}{11}-\dfrac{9}{11}\right)-\left(\dfrac{11}{13}-\dfrac{11}{13}\right)+\dfrac{13}{15}\)
\(=\dfrac{13}{15}\)

31​−53​+75​−97​+119​−1311​+1513​+1311​−119​+97​−75​+53​−31​
=(13−13)−(35−35)+(57−57)−(79−79)+(911−911)−(1113−1113)+1315=(31​−31​)−(53​−53​)+(75​−75​)−(97​−97​)+(119​−119​)−(1311​−1311​)+1513​
=1315=1513​

 

Bạn nên gõ đề bằng công thức toán (biểu tượng $\sum$ góc trái khung soạn thảo) để mọi người hiểu đề của bạn hơn nhé. 

\(=\left(-\dfrac{5}{9}-\dfrac{4}{9}\right)+\left(\dfrac{8}{15}+\dfrac{7}{15}\right)-\dfrac{2}{11}=-\dfrac{2}{11}\)

\(\dfrac{-5}{9}+\dfrac{8}{15}+\dfrac{-2}{11}+\dfrac{4}{-9}+\dfrac{7}{15}.\\ =\left(\dfrac{-5}{9}+\dfrac{-4}{9}\right)+\left(\dfrac{8}{15}+\dfrac{7}{15}\right)-\dfrac{2}{11}.\\ =-1+1-\dfrac{2}{11}.\\ =-\dfrac{2}{11}.\)

A=-5/7x2/11+-5/7x9/11+1+5/7

A=5/7x-2/11+5/7x-9/11+1+5/7

A=5/7x[-2/11+-9/11+1]+1

A=5/7x0+1

A=0+1

A=1

lí luận rõ ra nhé

A=\(\frac{-5}{7}\)x  \(\frac{2}{11}\)+  \(\frac{-5}{7}\)x  \(\frac{9}{11}\) +   \(1\frac{5}{7}\)

A= \(\frac{-5}{7}\)x (\(\frac{2}{11}\)+   \(\frac{9}{11}\)) +  \(\frac{12}{7}\)

A=  \(\frac{-5}{7}\)x 1 + \(\frac{12}{7}\)

A=  \(\frac{-5}{7}\)+    \(\frac{12}{7}\)

A=  1

\(=\left(\dfrac{9}{11}+\dfrac{20}{11}\right)+\left(\dfrac{5}{7}+\dfrac{2}{7}\right)+\dfrac{8}{13}\\ =\dfrac{29}{11}+1+\dfrac{8}{13}\) 

Biết đến đó thôi sorry:<

=(9/11+20/11)+(5/7+2/7)+8/13

=29/11+1+8/13

=377/143+1/143/143+88/143

=608/143

=(9/11+20/11)+(5/7+2/7)+8/13

=29/11+1+8/13

=377/143+143/143+88/143

=608/143