Question

1+6+11+16+..+121=? Ma ajuta careva ? Dau puncte ajutor pls

Answer 1

Suma creste din 5 in 5, il vom folosi pe 5 ca factor pentru fiecare element.

$1+6+11+16+...+121 = \\ \\ = (5\cdot 0+1)+(5\cdot 1+1) + (5\cdot 2+1)+ (5\cdot 3+1)+...+(5\cdot 14+1) = \\ \\ = 5\cdot 0+5\cdot 1+5\cdot 2+5\cdot 3+...+5\cdot 14+1+1+1+\underset{de~15~ori}{\underbrace{...}}+1 = \\ \\ = 5\cdot (0+1+2+3+...+14)+1\cdot 15 = \\ \\ = 5\cdot \dfrac{14\cdot (14+1)}{2}+15 = \\ \\ = 5\cdot \dfrac{14\cdot 15}{2}+15 = \\ \\ = 5\cdot 7\cdot 15+15 = \\ \\ = 15\cdot (5\cdot 7+1) = \\ \\ = 15\cdot (35+1) = \\ \\ = 15\cdot 36 = \\ \\ = 540$