Home
Class 12
MATHS
Let f(x)=(x+x^2+...+x^n-n)/(x-1), g(x)=(...

Let `f(x)=(x+x^2+...+x^n-n)/(x-1), g(x)=(4^n+5^n)^(1/n)` and `alpha` and `beta` are the roots of equation `lim_(x rarr 1) f(x)= lim_(n rarr oo) g(x)` then the value of `sum_(n=0)^oo (1/alpha+1/beta)^n` is

Text Solution

Verified by Experts

The correct Answer is:
`10/9`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    AAKASH INSTITUTE|Exercise Section - I|8 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE|Exercise SECTION - J ( Aakash Challengers Questions )|14 Videos

  • DETERMINANTS

    AAKASH INSTITUTE|Exercise SECTION - J|12 Videos

Similar Questions

Explore conceptually related problems

f(x)=(x+x^(2)+...+x^(n)-n)/(x-1),g(x)=(4^(n)+5^(n))^((1)/(n)) and alpha and beta are the roots of equation lim_(x rarr1)f(x)=lim_(n rarr oo)g(x) then the value of sum_(n=0)^(oo)((1)/(alpha)+(1)/(beta))^(n) is

lim_ (n rarr oo) (x ^ (n)) / (n!)

lim_(n rarr oo)(1+(x)/(n))^(n)

If f(x)=lim_(m rarr oo)lim_(n rarr oo)cos^(2m)n!pi x then the range of f(x) is

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

If f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1) then range of f(x) is

lim_ (n rarr oo) (1) / (1 + x ^ (n))

If lim_(n rarr oo)(1)/((sin^(-1)x)^(n)+1)=1, then find the value of x.

let f(x)=lim_(n rarr oo)(x^(2n)-1)/(x^(2n)+1)

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 :