Răspuns:
Explicație pas cu pas:
1 + 2 + 3 + 4 + ...... + 100 = 5 050
= 100 × ( 1 + 100 ) : 2 =
= 50 × 101 =
= 5 050
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5 + 10 + 15 + ...... + 1200 =
= 5×1 + 5×2 + 5 ×3 + ..... + 5 ×240 =
= 5 × ( 1 + 2 + 3 + ...... + 240 ) =
= 5 × [ 240 × ( 1 + 240 ) : 2] =
= 5 × ( 120 × 241 ) =
= 5 × 28 920 =
= 144 600
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111 + 222 + ..... + 999 =
= 111 × ( 1 + 2 + ...... + 9 ) =
= 111 × [ 9 × ( 1 + 9 ) : 2 ] =
= 111 × ( 9 × 10 : 2 ) =
= 111 × 45 =
= 4 995
_______________________
1 + 4 + 7 + 10 + ...... + 601 =
( 601-1):3+1 = 600:2+1=301 termeni are suma cu ratia 3 (4-1; 7-4...)
= 301 × ( 1 + 601 ) : 2 =
= 301 × 602 : 2 =
= 301 × 301 =
= 90 601
