Question

        Giúp mình câu này với :

                             2+2²+2³+...+2⁵⁰

mình sắp nộp bài rồi

Answer 1

Đặt S = 2 + 2^2 + 2^3 + ... + 2^50

S=2+2^2+2^3+...+2^50

2S= 2^2+2^3+...+2^51

=>2S ‐ S = ﴾ 2^2+2^3+...+2^51 ﴿ ‐ ﴾ 2+2^2+2^3+...+2^50 ﴿

= 2^51‐2 

Answer 2

\(\text{Đặt }A=2+2^2+2^3+...+2^{50}\)

=> \(2A=2^2+2^3+2^4+...+2^{51}\)

=> \(A=2A-A=\left(2^2+2^3+2^4+...+2^{50}\right)-\left(2+2^2+2^3+...+2^{50}\right)\)

=> \(A=2^{50}-2\)

Answer 3

Sửa lại xíu:

...

=> \(A=2A-A=\left(2^2+2^3+2^4+...+2^{51}\right)-\left(2+2^2+2^3+...+2^{50}\right)\)

=> \(A=2^2+2^3+2^4+...+2^{51}-2-2^2-2^3-...-2^{50}\)

=> \(A=2^{51}-2\)

Answer 4

Đặt \(A=2+2^2+2^3+...+2^{50}\), ta có:

       \(A=2+2^2+2^3+...+2^{50}\)

\(\Rightarrow2A=2\left(2+2^2+2^3+...+2^{50}\right)\)

\(\Rightarrow2A=4+2^3+2^4+...+2^{51}\)

\(\Rightarrow A=2A-A=\left(4+2^3+2^4+...+2^{51}\right)-\left(2+2^2+2^3+...+2^{50}\right)\)

\(\Rightarrow A=4+2^3+2^4+...+2^{51}-2-2^2-2^3-...-2^{50}\)

\(\Rightarrow A=2^{51}-2\) 

Chúc bạn học tốt.