Question

Tính tổng:

A=2⁰ + 2¹ + 2^{2 +}...+2⁴⁹ + 2⁵⁰

Answer 1

Ta có: \(A=2^0+2+2^2+...+2^{49}+2^{50}\)

  \(2A=2+2^2+2^3+...+2^{50}+2^{51}\)

\(2A-A=2^{51}-2^0\)

Hay \(A=2^{51}-1\)

Hok "tuốt" nha^^

Answer 2

\(A=1+2^1+2^2+...+2^{49}+2^{50}\)

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

\(2A-A=\left(2+2^2+2^3+...+2^{50}+2^{51}\right)-\left(1+2^1+2^2+...+2^{49}+2^{50}\right)\)

\(A=2^{51}-1\)

Answer 3

\(A=2^0+2^1+2^2+...+2^{49}+2^{50}\)

\(\Rightarrow2A=2+2^2+2^3+...+2^{50}+2^{51}\)

\(\Rightarrow2A-A=\left(2+2^2+2^3+...+2^{50}+2^{51}\right)-\left(2^0+2^1+2^2+...+2^{49}+2^{50}\right)\)

\(\Rightarrow A=2^{51}-1\)