Question

Care este formula la a^1+a^2+a^3+...+a^n

Answer 1

$S=1+a+a^2+a^3+...+a^n= \\ \\ ~~~ = \boxed{ \frac{a^{n+1}-1}{a-1} } \\ \\ Demonstratie:~ \\ \\ aS=a+a^2+a^3+a^4+...+a^{n+1} \\ S=1+a+a^2+a^3+...+a^n \\ \\ aS-S=a^{n+1}-1 \\ S(a-1)=a^{n+1}-1 \\ \\ \boxed{S= \frac{a^{n+1}-1}{a-1} }$