Réponse :
Bonjour!! :))
Exercice 1 :
D'abord, rappelvous 1 + 1/n = n/n + 1/n = (n + 1)/n
A = (1 + 1/2) X (1 + 1/3) X (1 + 1/4) + ................ + (1 + 1/9)
= 3/2 X 4/3 X 5/4 X 6/5 X 7/6 X 8/7 X 9/8 X 10/9 (2,3,4,5,6,7,8 et 9 annuler)
= 1/2 X 10
= 5
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Exercice 2
1) 1/p - 1/(p + 1)
= (p + 1) / (p*(p + 1)) - p / ((p + 1)*p) (Multiple le moins commun)
= ( p + 1 - p) / (p*(p + 1))
= 1/(p.(p + 1))
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2) 1 / 1(2) + 1/2(3) + 1/3(4) + .............. + 1/5004(5005)
= 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +.......... - 1/5004 + 1/5005 (De la 1er question)
= 1 + 1/5005
= 5005/5005 + 1/5005
= 5006/5005
Voilá
