Lời giải:
$A=(1+2-3-4-5)+(6+7-8-9-10)+(11+12-13-14-15)+....+(2011+2012-2013-2014-2015)+(2016+2017-2018-2019-2020)$

$=(-9)+(-14)+(-19)+....+(-2019)+(-2024)$

$=-(9+14+19+...+2019+2024)$

Số số hạng: $(2024-9):5+1=404$
$A=-(2024+9).404:2=-410666$

a, 921 + [ 97 + (-921) + ( -47)]

= 921 + 97 - 921 - 47

= (921 - 921) + (97 - 47)

= 50

b, 2013 + 2014 + 2015+ 2016 + ( -2017) + (-2018) + (-2019) + (-2020)

= 2013 + 2014 + 2015 + 2016 - 2017 - 2018 - 2019 - 2020

= (2013 - 2017) + (2014 - 2018) + (2015 - 2019) + (2016 - 2020)

= -4 - 4 - 4 - 4

= -16

Bài làm

a) 921 + [ 97 + (-921) + ( -47) ]

= 921 + 97 + ( -921 ) + ( -47 )

= [ 921 + ( -921 ) ] + [ 97 + ( -47 ) ]

= 0 + 50

= 50

b) 2013 + 2014 + 2015+ 2016 + ( -2017) + (-2018) + (-2019) + (-2020)

= [ 2013 + ( -2017 ) ] + [ 2014 + ( -2018 ) ] + [ 2015 + ( -2019 ) ] + [ 2016 + ( -2020 ) ]

=           -4                  +             ( -4 )           +            ( -4 )            +             ( -4 )

= -16

# Chúc bạn học tốt #

\(\dfrac{2013}{2013+2014}< \dfrac{2013}{2013+2013}=\dfrac{1}{2}\)

Tương tự cộng theo vế suy ra đpcm

chị kết bạn với em nha gửi lời kết bn với em nhé

j zậy em hả 

\(...=2022+2020+\left(-2019+2016-2018+2015-2017+2014\right)+...+\left(6-3+5-2+4-1\right)\)

\(=2022+2020+\left(-3-3-3\right)+\left(-3-3-3\right)+...+\left(-3-3-3\right)+\left(-3-2-1\right)\)

\(=2022+2020+\left(-9\right)+\left(-9\right)+...\left(-9\right)+\left(-6\right)\)

\(=2022+2020+\left(-9\right).\left[\left(2019-9\right):6+1\right].\left[\left(2019+6\right)\right]:2+\left(-6\right)\)

\(=2022+2020+\left(-9\right).336.2025:2+\left(-6\right)\)

\(=2022+2020-3061800-6\)

\(=-3057764\)

\(A=\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+...+\frac{1}{97\cdot99}-\frac{5}{4}\cdot\frac{13}{99}+\frac{5}{99}\cdot\frac{1}{4}\)

\(A=\frac{1}{2}\left(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{97\cdot99}\right)-\frac{13}{4}\cdot\frac{5}{99}+\frac{5}{99}\cdot\frac{1}{4}\)

\(A=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)-\frac{5}{99}\cdot\left(\frac{13}{4}-\frac{1}{4}\right)\)

\(A=\frac{1}{2}\left(\frac{1}{3}-\frac{1}{99}\right)-\frac{5}{99}\cdot3\)

\(A=\frac{1}{2}\cdot\frac{32}{99}-\frac{5}{33}\)

\(A=\frac{16}{99}-\frac{5}{33}=\frac{1}{99}\)

3/\(7a+b=0\Rightarrow b=-7a\)

\(f\left(x\right)=ax^2-7ax+c\).Ta có: \(f\left(10\right)=100a-70a+c=30a+c\)

\(f\left(-3\right)=30a+c\).Nhân theo vế ta có đpcm:

\(f\left(10\right).f\left(-3\right)=\left(30a+c\right)^2\ge0\) (đúng)

Câu 2 tự quy đồng rồi so sánh:v

S = 2020 + 2019 - 2018 - 2017 + 2016 + 2015 - 2014 - 2013 + ... + 4 + 3 - 2 - 1

= ( 2020 + 2019 - 2018 - 2017 ) + ( 2016 + 2015 - 2014 - 2013 ) + ... + ( 4 + 3 - 2 - 1 )   (có tất cả 2020 : 4 = 505 nhóm)

= 4 + 4 + ... + 4

= 4. 505 = 2020

Vậy S = 2020.

S= 2020

Bạn huyền đúng rồi đó .

hok tốt

S=2020