2002A= 2002 + \(2002^2+2002^3+2002^4+.....+2002^{100}\)

2002A - A= \(\left(2002+2002^2+2002^3+2002^4+....+2002^{100}\right)-\left(1+2002+2002^2+.....+2002^{99}\right)\)

2001A= \(2002^{100}-1\)

Vì \(2002^{100}\) > \(2002^{100}-1\) nên B > 2001A

2002a = \(2002+2002^2+...+2002^{100}\)

=> 2002a -a = \(2002^{100}-1

  Ta có \(B=2002^{100}\)

Ta có \(A=1+2002+2002^2+...+2002^{99}\)

         \(\Rightarrow2002A=2002+2002^3+...+2002^{100}\)

\(\Rightarrow2002A-A=\left(2002+2002^2+2002^3+...+2002^{100}\right)-\left(1+2002+2002^2+...+2002^{99}\right)\)

\(\Rightarrow2002A-A=2002+2002^2+2002^3+...+2002^{100}-1-2002-2002^2-...-2002^{99}\)

\(2001A=2002^{100}-1\)

                           vÌ 2002¹⁰⁰-1<2002¹⁰⁰ nên => A<B

                              ĐÚNG NHÉ

A < B nha bạn

k tui nha

thanks

a. 20​01^​2002 ​+2002^​2003​=[....1]+2002^​4.500​.2002^​3​=[..1]+[...6].[...8]=[...9].Vay 2001^​2002​+2002²⁰⁰³ k​o chia het cho2.

b.  861^​7​+972​^​2​=[....1]+[....4]=[....5].Vay 861^​7​+972^​2 chia het cho 5.​

\(\Leftrightarrow\left(a+2002\right)\left(b-2001\right)=\left(b+2001\right)\left(a-2002\right)\)

\(\Leftrightarrow ab-2001a+2002b-2002\cdot2001=ab-2002b+2001a-2001\cdot2002\)

=>-4002a=-4004b

hay a/2002=b/2001