Salut,
3 = 3·1 -- 1
5 = 3·2 -- 1
8 = 3·3 -- 1, deci termenul general ar fi 3·k -- 1.
Aflăm valoarea lui k pentru ultimul termen, adică 254 = 3k -- 1, deci 3k = 255, sau k = 255/3 = 85.
Suma are deci 85 de termeni, termenul general este 3·k -- 1:
[tex]\sum\limits_{k=1}^{85}(3k-1)=\sum\limits_{k=1}^{85}3k+\sum\limits_{k=1}^{85}(-1)=3\cdot\sum\limits_{k=1}^{85}k+85\cdot (-1)=\\\\\\=3\cdot\dfrac{85\cdot (85+1)}2-85=3\cdot 85\cdot\dfrac{86}2-85=85\cdot(3\cdot 43-1)=10880.[/tex]
Green eyes.
