Question

Rezolvati ecuatia:3+2×3+2×3²+2×3³+...+2×3 la puterea 2011=3×x-3

Answer 1

A=3(1+2+2·3+2·3² +......+2·3^2011)=3[1+2(1+3+3²+........3^2010)] =3[1+3^2011 - 1] =3^2012
S=1+3+3² +......+3^2010      3S =3+3² +3³ +........+3^2011
3S-S = 2S = 3^2011 - 1      S= (3^2011 - 1)/2
3^2012 = 3/(x³)  ⇒ 3^2012 ·x³ = 3 ⇒ 3^2011 ·x³ =1 ⇒
x³ =1/(3^2011)    x³ = (1/ 3^2011) ....undeva e o greseala ..... daca  ar fi x³ = 1/(3^2010) = 1/(3^670)³ ⇒ x=3^670
          sau x³ = 1/(3^2013) = 1/(3^671)³ ⇒x=3^671....vezi unde e greseala.....