If `a+alpha=1,b+beta=2` and `af(n)+alphaf(1/n)=bn+beta/n`, then find the value of `(f(n)+f(1/n))/(n+1/n)`

If   f(x ) = n/( n+1) , then find the value of f(n) + 1/f(n)

If alpha and beta are the roots of the equation x^(2)-3x-15=0 and (n)=alpha^(n)+beta^(n) then find the value of (f(8)-3f(7)+f(6))/(2f(6))

If alpha and beta are roots of the equation x^(2)-3x+1=0 and a_(n)=alpha^(n)+beta^(n)-1 then find the value of (a_(5)-a_(1))/(a_(3)-a_(1))

If alpha and beta are roots of x^(2)-x+2=0 and S_(n).=alpha^(n)+beta^(n),n in N ,then value of (sum_(n=1)^(5)s_(n))/(sum_(n=1)^(4)alpha^(n)+sum_(n=1)^(4)beta^(n)+7) is

Let alpha and beta be the roots of x^(2)-6x-2=0 with alpha>beta if a_(n)=alpha^(n)-beta^(n) for n>=1 then the value of (a_(10)-2a_(8))/(2a_(9))

If alpha,beta be the roots of x^(2)-x-1=0 and A_(n)=alpha^(n)+beta^(n), then A . M of A_(n-1) and A_(n), is

Let alpha and beta be the roots of x^(2)-5x+3=0 with alpha gt beta . If a_(n) = a^(n)-beta^(n) for n ge1 , then the value of (3a_(6)+a_(8))/(a_(7)) is :

If alpha and beta be root of x^2-6x-2=0 with alpha gt beta if a_n=alpha^n-beta^n for n ge 1 then the value of (a_(10)-2a_8)/(3a_9)

If (1)=1 and f(1)+2f(2)=3f(3)+......nf(n)=n(n+1)f(n) Then find the value of 49f(49)

If alpha,beta,gamma are the roots of the equation x^(3)-2x^(2)-1=0 and T_(n)=alpha^(n)+beta^(n)+gamma^(n) Find the value of (T_(11)-T_(8))/(T_(10))