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lolo555
@lolo555
July 2022
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Решите пожалуйста
1) (n+1)!/n! =6
2) n!/(n-2)!=6
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kmike21
Verified answer
N!=1*2*3*...*n
1) (n+1)!/n! =6
(n+1)!=n!(n+1), поэтому
(n+1)!/n!=
n!(n+1)/n!=
n+1
n+1=6
n=5
ответ:
n=5
2)n!/(n-2)!=6
n!=(n-2)!(n-1)n
n!/(n-2)!=(n-2)!(n-1)n/(n-2)!=(n-1)n=n²-n
n²-n=6
n²-n-6=0
D=1+4*6=25
√D=5
n₁=(1-5)/2=-2 -отпадает, так как n>0
n₂=(1+5)/2=3
Ответ: n=3
2 votes
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Answers & Comments
Verified answer
N!=1*2*3*...*n1) (n+1)!/n! =6
(n+1)!=n!(n+1), поэтому
(n+1)!/n!=n!(n+1)/n!=n+1
n+1=6
n=5
ответ: n=5
2)n!/(n-2)!=6
n!=(n-2)!(n-1)n
n!/(n-2)!=(n-2)!(n-1)n/(n-2)!=(n-1)n=n²-n
n²-n=6
n²-n-6=0
D=1+4*6=25
√D=5
n₁=(1-5)/2=-2 -отпадает, так как n>0
n₂=(1+5)/2=3
Ответ: n=3