[tex]\dfrac{1}{2^{3}} +\dfrac{1}{2^{2}} \cdot3 +\dfrac{1}{2} \cdot3^{2}+\dfrac{1}{3^{3}} =[/tex]
[tex]\dfrac{1}{8} +\dfrac{1}{4}\cdot3 +\dfrac{1}{2}\cdot9+\dfrac{1}{27}=[/tex]
[tex]\dfrac{1}{8} +\dfrac{3}{4} +\dfrac{9}{2}+\dfrac{1}{27}=[/tex]
[tex]\dfrac{1\cdot27+ 3\cdot54 +108\cdot9+1\cdot 8}{216}=[/tex]
[tex]\dfrac{27+162+972+8}{216}=[/tex] [tex]\dfrac{1169}{216}[/tex]
Daca scrierea era așa:
[tex]\bf \dfrac{1}{2^{3}} +\dfrac{1}{2^{2}\cdot3} +\dfrac{1}{2\cdot3^{2}}+\dfrac{1}{3^{3}}=[/tex]
[tex]\bf \dfrac{1}{8} +\dfrac{1}{4\cdot3} +\dfrac{1}{2\cdot9}+\dfrac{1}{27}=[/tex]
[tex]\bf \dfrac{1}{8} +\dfrac{1}{12} +\dfrac{1}{18}+\dfrac{1}{27}=[/tex]
[tex]\bf \dfrac{27+18+12+8}{216}=[/tex]
[tex]\bf \dfrac{65}{216}[/tex]
Bafta multa !
