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Ebls
@Ebls
May 2019
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Bonsoir pouvez vous m’aider s’il vous plaît
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MonsieurFirdown
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Bonsoir
♧1. On a :
1 /n − 1 /n+1
=>(n+1)-n /n(n+1)
=> 1 /n(n+1)
♧2. On a :
u(n+1)-u(n) ≤ 0
=> 1/(n+1)(n+2) - 1/n(n+1) ≤ 0
=> -2/n(n+1)(n+2) ≤ 0
● la suite u(n) est donc décroissante ...
♧3. Conjecture --> Lim( n -> +∞ ) u(n) = 0
♧4.
S(n) = 1 /1 - 1 /2 + 1 /2 − 1 /3 + … + 1 /n - 1 /n+1
S(n) = 1 - 1 (n+1)
lim ( n-> +∞ ) S(n) = 1
Voilà ^^
2 votes
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Verified answer
Bonsoir♧1. On a :
1 /n − 1 /n+1
=>(n+1)-n /n(n+1)
=> 1 /n(n+1)
♧2. On a :
u(n+1)-u(n) ≤ 0
=> 1/(n+1)(n+2) - 1/n(n+1) ≤ 0
=> -2/n(n+1)(n+2) ≤ 0
● la suite u(n) est donc décroissante ...
♧3. Conjecture --> Lim( n -> +∞ ) u(n) = 0
♧4.
S(n) = 1 /1 - 1 /2 + 1 /2 − 1 /3 + … + 1 /n - 1 /n+1
S(n) = 1 - 1 (n+1)
lim ( n-> +∞ ) S(n) = 1
Voilà ^^