\(A=20\times21+21\times22+...+99\times100\)

\(3\times A=20\times21\times\left(22-19\right)+21\times22\times\left(23-20\right)+...+99\times100\times\left(101-98\right)\)

\(=20\times21\times22-19\times20\times21+...+99\times100\times101-98\times99\times100\)

\(=99\times100\times101-19\times20\times21\)

Suy ra \(A=\frac{99\times100\times101-19\times20\times21}{3}=360640\)

\(B=3\times4\times5+4\times5\times6+...+98\times99\times100\)

\(4\times B=3\times4\times5\times\left(6-2\right)+4\times5\times6\times\left(7-3\right)+...+98\times99\times100\times\left(101-97\right)\)

\(=3\times4\times5\times6-2\times3\times4\times5+...+98\times99\times100\times101-97\times98\times99\times100\)

\(=98\times99\times100\times101-2\times3\times4\times5\)

Suy ra \(B=\frac{98\times99\times100\times101-2\times3\times4\times5}{4}=24497520\)

\(\dfrac{x+1}{99}+\dfrac{x+2}{98}+\dfrac{x+3}{97}+\dfrac{x+4}{96}=-4\)

\(\Rightarrow\dfrac{x+1}{99}+\dfrac{x+2}{98}+\dfrac{x+3}{97}+\dfrac{x+4}{96}+4=0\)

\(\Rightarrow\left(\dfrac{x+1}{99}+1\right)+\left(\dfrac{x+2}{98}+1\right)+\left(\dfrac{x+3}{97}+1\right)+\left(\dfrac{x+4}{96}+1\right)=0\)

\(\Rightarrow\dfrac{x+100}{99}+\dfrac{x+100}{98}+\dfrac{x+100}{97}+\dfrac{x+100}{96}=0\)

\(\Rightarrow\left(x+100\right)\left(\dfrac{1}{99}+\dfrac{1}{98}+\dfrac{1}{97}+\dfrac{1}{96}\right)=0\)

\(\Rightarrow x=-100\)(do \(\dfrac{1}{99}+\dfrac{1}{98}+\dfrac{1}{97}+\dfrac{1}{96}>0\))

e)20

f)27

g)9 hoặc -9

h)0 nhớ tik nha

Bài 1: 

a: Tổng là:

(-19+19)+(-18+18)+...+20=20

b: Tổng là:

-18+(-17+17)+...+0=-18

(x+1)/99 + (x+2)/98 + (x+3)/97 + (x+4)/96 = -4

=> [(x+1)/99 +1] +[(x+2)/98+1]+[(x+3)/97+1]+[(x+4)/96+1] = 0

=>[(x+100)/99] + [(x+100)/98] +[(x+100)/97] + [(x+100)/96]=0

=>(x+100)(1/99+1/98+1/97+1/96)=0

=>x+100=0

=>x= -100