Home
Class 12
MATHS
If "^(2n+1)P(n-1):^(2n-1)Pn=3:5, then fi...

If `"^(2n+1)P_(n-1):^(2n-1)P_n=3:5,` then find the value of `n`.

Text Solution

Verified by Experts

`.^(2n+1)P_(n-1): .^(2n-1)P_(n)=3:5`
or `(.^(2n+1)P_(n-1))/(.^(2n-1)P_(n))=(3)/(5)`
or `((2n+1)!)/((n+2)!)xx((n-1)!)/((2n-1)!)=(3)/(5)`
or `((2n+1)(2n))/((n+2)(n+1)n)=(3)/(5)`
or `10(2n+1)=3 (n+2)(n+1)`
or `3n^(2)-11n-4=0`
or (n-4)(3n+1)=0
or n=4
Promotional Banner

Similar Questions

Explore conceptually related problems

If .^(2n+1)P_(n-1): .^(2n-1)P_(n)=3:5 , find n.

If .^(n+r+1)P_(2)=72and.^(n-r)P_(2)=12 then find the values of n and r.

If .^(n+1)P_(4):^(n-1)P_(3)=72:5 , find n.

If ^ n P_5 = 20 ^nP_3 find the value of n

Let S_(n) be the sum of first n terms of an A.P. If S_(2n) = 5s_(n) , then find the value of S_(3n) : S_(2n) .

If a_(1)=1 and a_(n+1)=(4+3a_(n))/(3+2a_(n)),nge1"and if" lim_(ntooo) a_(n)=a,"then find the value of a."

If f(n+1)=(2f(n)+1)/(2),n=1,2,3,... and f(1)=2 then find the value of f(101).

If .^(n+1)P_(3)=10.^(n-1)P_(2) , find n.

If (1+x+x^2++x^p)^n=a_0+a_1x+a_2x^2++a_(n p)x^(n p), then find the value of a_1+2a_2+3a_3+ddot+n pa_(n p)dot

If .^(n)P_(5)=20.^(n)P_(3) , find n.