Question

if 2n+1 pn-1 :2n-1 pn = 3:5 find n??
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Answer 1

Answer:

Given equation is 2n+1Pn−1:2n−1Pn=3:5

So,(2n−1−n)!(2n−1)!(2n+1−n+1)!(2n+1)!=53

⇒(n+2)(n+1)n(n−1)!(2n+1)(2n)(2n−1)!×(2n−1)!(n−1)!=53

Solving we get

⇒(n+1)(n+2)2(2n+1)=53

⇒20n+10=3n2+9n+6

⇒3n2−11n−4=0

⇒3n2−12n+n−4=0

⇒3n(n−4)+1(n−4)=0

∴n=4