Question

cho a=2+2²+2³+.....+2¹⁰chứng tỏ a+2=2¹¹

Answer 1

Ta có :

\(A=2+2^2+2^3+...........+2^{10}\)

\(\Leftrightarrow2A=2^2+2^3+.........+2^{11}\)

\(\Leftrightarrow2A-A=\left(2^2+2^3+......+2^{11}\right)-\left(2+2^2+....+2^{10}\right)\)

\(\Leftrightarrow A=2^{11}-2\)

\(\Leftrightarrow A+2=2^{11}\left(đpcm\right)\)

Answer 2

A = 2 + 2² + 2³ + ... + 2¹⁰

=> 2A = 2² + 2³ + ... + 2¹¹

=> 2A - A = 2¹¹ - 2

=> A = 2¹¹ - 2

Thay vào bài ra ta được : 2¹¹ - 2 + 2 = 2¹¹ (đpcm)

Answer 3

Ta có :

A=2+2²+2³+.....+2¹⁰

\(\Leftrightarrow\)2A=2²+2³+.....+2¹¹

\(\Leftrightarrow\)2A-A=(2²+2³+.....+2¹¹)-(2+2²+2³+.....+2¹⁰)

\(\Leftrightarrow\)A=2¹¹-2

​Vậy A+2=2¹¹