Question

1 + 2^2 +  2^4 + ... +2^30 = ??

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Answer 1

Đặt A= \(1+2^2+2^4+...+\)\(2^{30}\)

\(\Rightarrow2^2.A=2^2.\left(1+2^2+2^4+...+2^{30}\right)\)

\(\Rightarrow4A=2^2+2^4+2^6+...+2^{30}+2^{32}\)

\(\Rightarrow4A-A=\left(2^2+2^4+2^6+...+2^{30}+2^{32}\right)-\left(1+2^2+2^4+...+2^{30}\right)\)

\(\Rightarrow3A=2^{32}-1\)

\(\Rightarrow A=\frac{2^{32}-1}{3}\)