a) 80 + 82 + 84 + 86 +......+ 264 =
= 2(40+41+42+43+...+132) =
= 2[(1+2+3+...+132)-(1+2+3+...+39) =
= 2(132×133:2-39×40:2) =
= 2(66×133 - 39×20) =
= 2(8778 - 780) =
= 2 × 7998 =
= 15 996
b) 7 + 16 + 25 + 34 +......+ 862 =
= 9×1-2 + 9×2-2 + 9×3-2 + 9×4-2 + ...+
9×96-2 =
= 9(1+2+3+4+...+96) - 2+2+2...+2 (de 96 ori) =
= 9 ( 96×97:2) - 2× 96 =
= 9 (97×48) - 192 =
= 9 × 4656 - 192 =
= 41904 - 192 =
= 41712
c) 54 + 63 + 72 + 81 +......+ 675 =
= 9 ( 6+7+8+9+...+ 75) =
= 9 [ (1+2+3+...75) - 1+2+...+5)] =
= 9 ( 75×76:2 - 5×6:2) =
= 9 ( 75×38 - 15) =
= 9 (2850-15) =
= 9 × 2835 =
= 25 515
d) se rezolva la fel ca b)
37 = 6×6+1
43 = 6×7+1
.......
