Question

Calculeaza suma data S=2+5+8+...+254 folosind simbolul sigma.

Answer 1

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:

$\sum\limits_{k=1}^{85}(3k-1)=\sum\limits_{k=1}^{85}3k+\sum\limits_{k=1}^{85}(-1)=3\cdot\sum\limits_{k=1}^{85}k+85\cdot (-1)=\\\\\\=3\cdot\dfrac{85\cdot (85+1)}2-85=3\cdot 85\cdot\dfrac{86}2-85=85\cdot(3\cdot 43-1)=10880.$

Green eyes.