Question

A=13+12x13+12x13^2+....+12×13^2003
Aratati ca A=13^2004
Vreau si rezolvare

Answer 1

A=13+12·13(1+13+13²+...........$13^{2002}$)
paranteza este o progresie geometrica cu primul termen 1 si ratia 13.
suma primilor n termeni ai unei progresii geometrice= $b_{1}$·$\frac{ q^{n}-1 }{q-1}$
$S_{2003}$=1·$\frac{ 13^{2003}-1 }{13-1}$
A=13+12·13·$\frac{ 13^{2003}-1 }{12}$=13+13($13^{2003}$-1)=
= 13+$13^{2004}$-13=$13^{2004}$