Question

Calculați sumele s1=1+3+3^2+3^3+....+3^50.

Answer 1

eo formula se face in liceu
bine e sa o inveti pe d rost
1+a+a²+..+a^n=(a^(n+1)-1)/(a-1)

deci in cazul nostru s1=
(3^51-1)/(3-1)=(3^51-1)/2

Answer 2

[tex]\it S = 1+3+3^2+3^3 +\ ...\ +3^{49} +3^{50} \\\;\\ 3S = 3+3^2+3^3+\ ...\ + 3^{50}+3^{51} [/tex]

$\it 3S-S = 3^{51}-1\Rightarrow 2S = 3^{51}-1\Rightarrow S=(3^{51}-1):2$