Question

2) Rút gọn A=1+2+2^2+... +2^25 B=1+3+3^2+... +3^19

Answer 1

\(A=1+2+2^2+...+2^{25}\)

\(2A=2+2^2+2^3+...+2^{26}\)

\(2A-A=A=2^{26}-1\)

 

\(B=1+3+3^2+...+3^{19}\)

\(3B=3+3^2+3^3+...+3^{20}\)

\(3B-B=3^{20}-1\)

\(B=\dfrac{3^{20}-1}{2}\)

Answer 2

a: A=1+2+2^2+...+2^25

=>2A=2+2^2+...+2^26

=>A=2^26-1

b: B=1+3+3^2+...+3^19

=>3B=3+3^2+3^3+...+3^20

=>2B=3^20-1

=>B=(3^20-1)/2