Răspuns:
Explicație pas cu pas:
[tex]\bf S=7^{51} + 7^{52} +7^{53}+7^{54}+....+7^{80}[/tex]
[tex]\bf S=\Big(7^{51} + 7^{52} \Big)+\Big(7^{53}+7^{54}\Big)+ ...+\Big(7^{79}+7^{80}\Big)[/tex]
[tex]S=7^{51}\cdot \Big(7^{51-51} + 7^{52-51} \Big)+7^{53}\cdot \Big(7^{53-53}+7^{54-53}\Big)+ ...+7^{79}\cdot \Big(7^{79-79}+7^{80-79}\Big)[/tex]
[tex]\bf S=7^{51}\cdot \Big(7^{0} + 7^{1} \Big)+7^{53}\cdot \Big(7^{0}+7^{1}\Big)+ ...+7^{79}\cdot \Big(7^{0}+7^{1}\Big)[/tex]
[tex]\bf S=7^{51}\cdot \Big(1 + 7 \Big)+7^{53}\cdot \Big(1 + 7\Big)+ ...+7^{79}\cdot \Big(1 + 7\Big)[/tex]
[tex]\bf S=7^{51}\cdot 8+7^{53}\cdot 8+ ...+7^{79}\cdot 8[/tex]
[tex]\bf S=8\cdot \Big(7^{51}+7^{53}+ ...+7^{79}\Big)[/tex]
[tex]\red{\boxed{\bf ~S=2^{3} \cdot \Big(7^{51}+7^{53}+ ...+7^{79}\Big)~\vdots~2~}}[/tex]
[tex]==pav38==[/tex]
