2npn+1:2n-2pn=56:3 find n
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Given equation is
2n+1
P
n−1
:
2n−1
P
n
=3:5
So,
(2n−1−n)!
(2n−1)!
(2n+1−n+1)!
(2n+1)!
=
5
3
⇒
(n+2)(n+1)n(n−1)!
(2n+1)(2n)(2n−1)!
×
(2n−1)!
(n−1)!
=
5
3
Solving we get
⇒
(n+1)(n+2)
2(2n+1)
=
5
3
⇒20n+10=3n
2
+9n+6
⇒3n
2
−11n−4=0
⇒3n
2
−12n+n−4=0
⇒3n(n−4)+1(n−4)=0
∴n=4
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