Question

Rút gọn :  A = 2^100 - 2^99 + 2^98 - 2^97 + ... + 2^2 - 2

Answer 1

\(A=2^{100}-2^{99}+2^{98}-2^{97}+...+2^2-2\)

\(\Rightarrow2A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2\)

\(\Rightarrow2A+A=2^{101}-2^{100}+2^{99}-2^{98}+...+2^3-2^2+2^{100}-2^{99}-2^{98}-2^{97}+...+2^2-2\)

\(\Rightarrow3A=2^{201}-2\)

\(\Rightarrow\)\(\frac{2^{201}-2}{3}\)

Answer 2

mình lấy cả 2 nick tích cho nguyên linh đấy

Answer 3

h minh di

Answer 4

tích lại đi

Answer 5

\(2A=2^{101}-2^{100}+...+2^3-2^2\)

\(A=2^{100}-2^{99}+...+2^2-2\)

\(\Rightarrow3A=2A+A=2^{101}-2\)

\(\Rightarrow A=\frac{2^{101}-2}{3}\)

Answer 6

được của ló