Question

1+2+2^2+2^3+...+2^2002




va rogggg​

Answer 1

$S= 1 + 2 {}^{1} + {2}^{2} + {2}^{3} + ... + {2}^{2002} \\ 2S= 2 + 2 {}^{2} + 2 {}^{3} + ... + 2 {}^{2003} \\ \\ 2S = (1 +2 + 2 {}^{2} + ... + 2 {}^{2002} ) + 2 {}^{2003} - 1 \\ 2S = S + 2 {}^{2003} - 1 \\ 2S - S = 2 {}^{2003} - 1 \\ S = 2 {}^{2003} - 1$