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andre99
@andre99
June 2021
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(1+1/2) (1+1/3)(1+1/4) x ...x (1+ 1/1999)
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editions
Bonjour
1+1/2=3/2
1+1/3=4/3
.
.
1+1/1999=2000/1999
donc
(1+1/2) (1+1/3)(1+1/4) x ...x (1+ 1/1999)
=(3/2)*(4/3)*....*1998*1999*1999/2000
=(3*4*.........*1999)/(2*3*4*......*1999*2000)
en simplifiant ça donne 2000/2=1000
1 votes
Thanks 1
andre99
dernière parenthèse est pas resté deux multiplié par 2000
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1+1/2=3/2
1+1/3=4/3
.
.
1+1/1999=2000/1999
donc
(1+1/2) (1+1/3)(1+1/4) x ...x (1+ 1/1999)=(3/2)*(4/3)*....*1998*1999*1999/2000
=(3*4*.........*1999)/(2*3*4*......*1999*2000)
en simplifiant ça donne 2000/2=1000