If `(a^n+b^n)/(a^(n-1)+b^(n-1))` is the A.M. between a and b, then find the value of n.

Find n such that (a^n+b^n)/(a^(n-1)+b^(n-1)) may be the geometric mean between two quantities a and b.

Find n, so that (a^(n+1)+b^(n+1))/(a^(n)+b^(n))(a ne b ) be HM beween a and b.

Find the value of n so that (a^(n+1)+ b^(n+1))/(a^n+b^n) may be the geometric mean between a and b.

If A = [[1 ,1],[1,1]] and det (A^(n) - 1) = 1 -lambda ^(n), n in N, then the value of lambda is

Find the value of n so that (a^(n+1)+b^(n+1))/(a^n+b^n) may be the geometric mean between a and b .

If .^(n+1)C_(r+1):^(n)C_(r):^(n-1)C_(r-1)=11:6:3 , find the values of n and r.

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

If |[ x^n ,x^(n+2) ,x^(2n)],[1 ,x^a , a ],[x^(n+5),x^(a+6),x^(2n+5)]|=0,AAx in R, where . n in N , then value of a is a. n b. n-1 c. n+1 d. none of these

The nth term of a series is given by t_(n)=(n^(5)+n^(3))/(n^(4)+n^(2)+1) and if sum of its n terms can be expressed as S_(n)=a_(n)^(2)+a+(1)/(b_(n)^(2)+b) where a_(n) and b_(n) are the nth terms of some arithmetic progressions and a, b are some constants, prove that (b_(n))/(a_(n)) is a costant.

If (n!)/(2!(n-2)!):(n!)/(4!(n-4)!) =2:1 . Find the value of n.