Question

calculati suma 3+9+27+.....+6561

Answer 1

$S_n =3+9+27+...+6561$
$S_n =3^1+3^2+3^3+...+3^n$

Observam ca n-ul de la puterea ultimului termen, reprezinta chiar numarul de termeni.

$b_1 = 3 \\ q=3 \\ b_n=6561=3^n=q^n \\ \\ S_n = b_1\cdot \frac{q^n-1}{q-1}$

$q^n = 3^n = 6561 \\ \\ \Rightarrow S_n = 3\cdot \frac{6561-1}{3-1} \Rightarrow S_n = 3\cdot \frac{6560}{2} \Rightarrow S_n = 3\cdot3280 \Rightarrow S_n = 9840$