Home
Class 12
MATHS
if a(n=(alpha^(n)-beta^(n))/(alpha-beta)...

if `a_(n=(alpha^(n)-beta^(n))/(alpha-beta)` where `alpha` and `beta` are roots of equation `x^(2)-x-1=0` and `b_(n)=a_(n+1)+a_(n-1)` then

A

`sum_(n=1)^(oo) (b_(n))/(10^(n)) = (8)/(89)`

B

`b_(n) = alpha^(n) + beta^(n) ` for all ` n ge 1 `

C

` a_(1) + a_(2) + a_(3) + …+ a_(n) = a_(n+2) -1 ` for all ` n ge 1` .

D

`sum_(n=2)^(oo) (a_(n))/(10^(n)) = (10)/(89)`

Text Solution

Verified by Experts

The correct Answer is:
BCD
Promotional Banner

Similar Questions

Explore conceptually related problems

If alpha and beta are the roots of the equation x^(2)-ax+b=0 and A_(n)=alpha^(n)+beta^(n)

alpha and beta are the roots of x^2-x-1=0 and S_n=2023 alpha^n 2024 beta^n then

If alpha and beta are the roots of the equation x^(2)-ax+b=0 and A_(n)=alpha^(n)+beta^(n), then which of the following is true?

If alpha and beta are the roots of the equation x^(2)-ax+b=0 and A_(n)=alpha^(n)+beta^(n), then which of the following is true?

Find the value of x such that ((x+alpha)^(n)-(x+beta)^(n))/(alpha-beta)=(sin(n theta))/(sin^(n)theta), where alpha and beta are the roots of the equation t^(2)-2t+2=0

Let alpha and beta be the roots of the equation 5x^2+6x-2=0 . If S_n=alpha^n+beta^n, n=1,2,3.... then

If ""_(alpha)and _(beta) are the roots of equation x^(2)-3x+1=0and a_(n)=alpha^n+beta^(n),ninN then value of (a_(7)+a_(5))/(a_(6))=

If alpha,beta are the roots of x^(2)-2x+4=0 then alpha^(n)+beta^(n) is