Răspuns:
Explicație pas cu pas:
Calculati:
a)2+4+6+...+100= 2×(1+2+3+.....+50) = 2 × 50 ×(1+50)/2 = 50×51 = 2550
b)3+6+9+...+90= 3×(1+2+3+.......+30)=3×30×(1+30):2=45×31=1395
c)2+4+6+...+2004= 2×(1+2+3+....+1002) = 2 × 1002 × 1003 : 2 = 1002×1003 = 1005006
d)3+6+9+...+2001= 3×(1+2+3+ .....+667)=3×667×668:2=2001×334=
= 668334
e)5+10+15+...+105= 5×(1+2+3+.....+21)=5×21×22:2=105×11=1155
f)100+200+...+8000= 100×(1+2+...+80)=100×80×81:2=4000×81=324000
a)
2 + 4 + 6 + ... + 100 = ?
2 × (1 + 2 + 3 + ... + 50) = 2550
2 × [50 × (50 + 1) ÷ 2] = 2550
2 × (50 × 51 ÷ 2) = 2550
2 × (2550 ÷ 2) = 2550
2 × 1275 = 2550
b)
3 + 6 + 9 + ... + 90 = ?
3 × (1 + 2 + 3 + ... + 30) = 1395
3 × [30 × (30 + 1) ÷ 2] = 1395
3 × (30 × 31 ÷ 2) = 1395
3 × (930 ÷ 2) = 1395
3 × 465 = 1395
c)
2 + 4 + 6 + ... + 2004 = ?
2 × (1 + 2 + 3 + ... + 1002) = 1005006
2 × [1002 × (1002 + 1) ÷ 2] = 1005006
2 × (1002 × 1003 ÷ 2) = 1005006
2 × (1005006 ÷ 2) = 1005006
2 × 502503 = 1005006
d)
3 + 6 + 9 + ... + 2001 = ?
3 × (1 + 2 + 3 + ... + 667) = 668334
3 × [667 × (667 + 1) ÷ 2] = 668334
3 × (667 × 668 ÷ 2) = 668334
3 × (445556 ÷ 2) = 668334
3 × 222778 = 668334
e)
5 + 10 + 15 + ... + 105 = ?
5 × (1 + 2 + 3 + 21) = 1155
5 × [21 × (21 + 1) ÷ 2] = 1155
5 × (21 × 22 ÷ 2) = 1155
5 × (462 ÷ 2) = 1155
5 × 231 = 1155
f)
100 + 200 + ... + 8000 = ?
100 × (1 + 2 + ... + 80) = 324000
100 × [80 × (80 + 1) ÷ 2] = 324000
100 × (80 × 81 ÷ 2) = 324000
100 × (6480 ÷ 2) = 324000
100 × 3240 = 324000
