If `alpha` and `beta` are the roots of the equation `375x^(2)-25x-2=0`, then the value of `lim_(n rarr oo)(sum_(r=1)^(n)alpha^(r)+sum_(r=1)^(n)beta^(r))` is

lim_(x rarr2)(sum_(r=1)^(n)x^(r)-sum_(r=1)^(n)2^(r))/(x-2)

lim_(n rarr oo) sum_(r=0)^(n-1) 1/(n+r) =

If alpha and beta are the roots of the equation 375 x^(2) - 25x - 2 = 0 , then lim_(n to oo) Sigma^(n) alpha^(r) + lim_(n to oo) Sigma^(n) beta^(r) is equal to :

If alpha and beta are the roots of the equation 375 x^(2) - 25x - 2 = 0 , then lim_(n rarr oo) Sigma_(r = 1)^n alpha^(r) + lim_(n rarr oo) Sigma_(r = 1)^n beta^(r) is equal to :

Find the value of lim_(n rarr oo)sum_(r=1)^(n)(r^(2))/(n^(3)+n^(2)+r)

If alpha and beta are the roots of the quadratic equation 4x ^(2) + 2x -1=0 then the value of sum _(r =1) ^(oo) (a ^(r ) + beta ^(r )) is :

If alpha and beta are the roots of the quadratic equation 4x ^(2) + 2x -1=0 then the value of sum _(r =1) ^(oo) (a ^(r ) + beta ^(r )) is :

lim_(n rarr oo)(1)/(n^(4))sum_(r=1)^(n)r^(3)=

if alpha,beta be roots of equation 375x^(2)-25x-2=0 and s_(n)=alpha^(n)+beta^(n) then lim_(n rarr oo)(sum_(r=1)^(n)S_(r))=......