Let `agtbgt0` and `I(n)=a^((1)/n)-b^((1)/(n)),J(n)=(a-b)^((1/(n))` for all `nge2`. Then

Let a lt b lt 0 and I(n) =a^(1//n)-b^(1//n),J(n)=(a-b)^(1//n) for all n ge 2 then

Show that (1-i)^(n)(1-(1)/(i))^(n)=2^(n) for all n in N

What is lim_(ntooo)(a^(n)+b^(n))/(a^(n)-b^(n)) where agtbgt1 , equal to?

Let alpha,beta be the roots of x^(2)-x-1=0ands_(n)=alpha^(n)+beta^(n) for all integers nge1 . Then for every integer nge2 -

The value of lim_(nto oo)(a^(n)+b^(n))/(a^(n)-b^(n)), (where agtbgt1 is

The value of lim_(nto oo)(a^(n)+b^(n))/(a^(n)-b^(n)), (where agtbgt1 is

Prove that i^(n)+i^(n+1)+i^(n+2)+i^(n+3)=0 for all n inN

Let A=[(1,1,1),(0,1,1),(0,0,1)] prove that by induction that A^n=[(1,n,n(n+1)/2),(0,1,n),(0,0,1)] for all n in N .