Răspuns:
Explicație pas cu pas:
2 + 3 + 4 + ......+ 30 = 464
1 + ( 2 + 3 + 4 + ..... + 30 ) - 1 =
= 30 × ( 1 + 30 ) : 2 - 1 =
= 15 × 31 - 1 =
= 465 - 1 =
= 464
Sau:
2 + 3 + 4 + ...... + 30 = 464
-> aflu numarul termenilor sumei:
30 - 2 + 1 = 28 + 1 = 29 termeni are suma
= 29 × ( 2 + 30 ) : 2 =
= 29 × 32 : 2 =
= 29 × 16 =
= 464
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b)
9 + 10 + 11 + .... + 30 =
= 1+2+3+4+5+6+7+8+ (9+10+11+...+30) - ( 1+2+3+...+8) = 429
-> aplic formula sumei lui Gauss: nr. termeni ×(primul teremen + ultimul):2
= 30 × ( 1 + 30 ) : 2 - ( 8 × 9 : 2 ) =
= 15 × 31 - 36 =
= 465 - 36 =
= 429
Sau:
9 + 10 + 11 + ... + 30 = 429
-> aflam cati termeni are suma
30 - 9 + 1 = 22 termeni are suma
= 22 × ( 9 + 30 ) : 2 =
= 11 × 39 =
= 429
