Răspus:
Explicație pas cu pas:
1 + 3 + 5 + ...... + 99 =
-> stabilesc cati termeni are suma numerelor impare
(99 -1) : 2 + 1 = 98 : 2 + 1 = 50 de termeni
= 50 × ( 1 + 99 ) : 2 =
= 50 × 100 : 2 =
= 50 × 50 =
= 2 500
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Sau:
(1 + 2 + 3 + ...... + 98 + 99 )- (2+4 +.....+98) =
-> aplic formula sumei lui Gauss:
= nr. termeni x suma dintre primul si ultimul termen : 2
= 99 × (1+99):2 - 2 × (1+2+....+49) =
= 99 × 100 : 2 - 2 × 49 × (1+49): 2 =
= 99 × 50 - 49 × 50 =
= 50 × ( 99 - 49 ) =
= 50 × 50 =
= 2 500
