Question

Va rog mă ajutați la mate.
S=2+2²+2³+......+2la puterea 40

Answer 1

$S=2+ 2^{2} + 2^{3} +...+ 2^{40} |*2 \\ 2S= 2^{2} + 2^{3} +...+ 2^{40}+ 2^{41} \\ 2S-S= 2^{41} -2 \\ S=2^{41} -2$

Answer 2

$S=2+2^2+2^3+...+2^4^0| \cdot 2 \\ 2S=2^2+2^3+2^4+...+2^4^0+2^4^1 \\ 2S-S=2^2+2^3+2^4+...+2^4^0+2^4^1-(2+2^2+2^3+...+2^4^0) \\ S=2^2+2^3+2^4+...+2^4^0+2^4^1-2-2^2-2^3-...-2^4^0 \\ S=2^4^1-2 \\ S=2(2^4^0-1)$