Question

Rút gọn biểu thức sau:

B = 1+ 2² + 2⁴ + 2⁶ +.....+ 2¹⁸

Answer 1

Ta có: \(B=1+2^2+2^4+.....+2^{18}\)

\(\Rightarrow2B=2+2^3+2^5+...+2^{19}\)

\(\Rightarrow2B-B=\left(2+2^3+2^5+....+2^{19}\right)-\left(1+2^2+2^4+...+2^{18}\right)\)

\(\Rightarrow B=2^{19}-1\)

Vậy rút gọn biểu thức \(B=1+2^2+2^4+...+2^{18}\) được \(2^{19}-1\)

Answer 2

B  =1+2^2+2^4+2^6+...+2^18

    =2^0+2^2+2^4+2^6+...+2^18

4B=2^2+2^4+2^6+2^8+...+2^20

4B-B=(2^2+2^4+2^6+2^8+...+2^20)-(2^0+2^2+2^4+2^6+...+2^18)

3B=2^2+2^4+2^6+2^8+...+2^20-2^0-2^2-2^4-2^6-...-2^18

3B=2^20-2^0

3B=2^20-1

B=(2^20-1)/3