Question

Tính tổng: 2^1+2^3+2^5+...+2^99

Answer 1

\(A=2^1+2^3+2^5+...+2^{99}\)

\(4A=2^3+2^5+2^7+...+2^{101}\)

\(4A-A=\left(2^3+2^5+2^7+...+2^{101}\right)-\left(2^1+2^3+2^5+...+2^{99}\right)\)

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

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