y = 1+9+17+...+2009
(observam ca, creste cu 8, aflam numarul de termeni:)
n=1 -> 1:8 = cat 0. -> n = 0+1 = 1
n=2 -> 9:8 = cat 1 -> n = 1+1 = 2
n=3 -> 17:8 = cat 2 -> n = 2+1 = 3
......
n=? -> 2009:8 = cat 251 -> n = 251+1 => n = 252
y = 1+9+17+...+2009 => y = (1+1)+(9+1)+(17+1)+...+(2009+1) - 252 =>
=> y = 2+10+18+...+2010 - 252 => y = 2×(1+5+9+...+1005) - 252 =>
=> y = 2×[1+(2+3)+(4+5)+...+(502+503)] - 252 => [tex]y = 2\times \frac{503\cdot504}{2}-252 [/tex]
=> y = 503×504 - 252 => y = 253260
