1
a)7!-5!=5!*6*7-5!=5!*(42-41=1*2*3*4*5*41=120*41=4920
b)24!/(20!*4!)=20!*21*22*23*24/(20!*1*2*3*4)=21*22*23=10626
2
(n+1)!/(n+3)!=(n+1)!/((n+1)!*(n+2)(n+3))=1/(n²+5n+6)
3
(3n-4)!=20*(3n-5)!
(3-5)!*(3n-4)-20*(3n-5)!=0
(3n-5)!*(3n-4-20)=0
3n-5=0⇒3n=5⇒n=5/3∉N
3n-24=0⇒3n=24⇒n=8
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1
a)7!-5!=5!*6*7-5!=5!*(42-41=1*2*3*4*5*41=120*41=4920
b)24!/(20!*4!)=20!*21*22*23*24/(20!*1*2*3*4)=21*22*23=10626
2
(n+1)!/(n+3)!=(n+1)!/((n+1)!*(n+2)(n+3))=1/(n²+5n+6)
3
(3n-4)!=20*(3n-5)!
(3-5)!*(3n-4)-20*(3n-5)!=0
(3n-5)!*(3n-4-20)=0
3n-5=0⇒3n=5⇒n=5/3∉N
3n-24=0⇒3n=24⇒n=8
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1
a)(8!-6!):330=(6!*7*8-6!):330=6!*(56-1):330=6!*55/330=6!/6=
=1*2*3*4*5*6/6=120
b)15!/(12!*3!)=12!*13*14*15/(12!*1*2*3)=13*7*5=455
2
(n+1)!/(n*(n-2)!)=(n-2)!*(n-1)*n*(n+1)/(n*(n-2)!)=(n-1)(n+1)=n²-1
3
(n+2)!=42*n!
n!*(n+1)(n+2)-42*n!=0
n!*(n²+3n+2-42)=0
n=0∉N
n²+3n-40=0
n1+n2=-3 U n1*n2=-40
n=-8∉N
n=5