Question

Giúp mình với A=1+ 2 mũ 2+ 2 mũ 3+...+ 2 mũ 10 . Cảm ơn trc ạ ^^

Answer 1

`A=1+2^2 +2^3 +...+2^10`

`2A=2+2^3 +2^4 +...+2^11`

`A=2+2^3 +2^4 +...+2^11 -1-2^2 -2^3 -...-2^10`

`A=2+2^11 -1-2^2`

`A=2+2048-1-4`

`A=2045`

Answer 2

Đặt: \(A=1+2^2+2^3+...+2^{10}\)

\(\Rightarrow2A=2\cdot\left(1+2^2+2^3+...+2^{10}\right)\)

\(\Rightarrow2A=2+2^3+2^4+...+2^{11}\)

\(\Rightarrow2A-A=\left(2+2^3+2^4+...+2^{11}\right)-\left(1+2^2+2^3+...+2^{10}\right)\)

\(\Rightarrow A=2+2^3+2^4+...+2^{11}-1-2^2-2^3-...-2^{10}\)

\(\Rightarrow A=\left(2^3-2^3\right)+\left(2^4-2^4\right)+...+\left(2^{10}-2^{10}\right)+\left(2+2^{11}-1-2^2\right)\)

\(\Rightarrow A=0+0+0+...+2+2^{11}-1-2^2\)

\(\Rightarrow A=2+2^{11}-1-4\)

\(\Rightarrow A=2^{11}-3\)