[tex]\displaystyle \\
8+8^2+8^3+\cdots+8^{42} \\
\text{Sirul are 42 de termeni.} \\
\text{Rescriem sirul cu mai multi termeni:} \\
8+8^2+8^3+8^4+8^5+8^6+\cdots+8^{40}+8^{41}+8^{42} \\ \\
\text{Rezolvare: }\\ \\
\text{Observam ca suma primilor 3 termeni, se divide cu 73.} \\
8+8^2+8^3= 8(1+8+8^2)=8(1+8+64)= (8\times 73) ~\vdots ~73 \\ \\
\text{Grupam termenii sirului in grupe de cate 3 termeni.} \\ \\
\text{Avem voie deoarece numarul de termeni este divizibil cu 3} [/tex]
[tex]\displaystyle \\
(8+8^2+8^3)+(8^4+8^5+8^6)+\cdots+(8^{40}+8^{41}+8^{42}) = \\ \\
8(1 + 8+8^2) + 8^4(1 + 8+8^2)+\cdots+8^{40}(1 + 8+8^2) = \\ \\
8\times 73 + 8^4 \times 73 +\cdots+8^{40}\times 73 = \\
73(8 + 8^4 +\cdots+8^{40}) ~\vdots~73 \\ \\
cctd[/tex]
