if we have
sum{n=0/to infinit} f_n (x)
such that n in N and x in [-1.1]
f_n =x/(1+x^2)^n
r this series confergence?is it uniform convergence?
Ya have,Originally Posted by sweet
Thus, and apply the ratio test,
This gives,
It converges absolutely when,
Thus,
Thus, .
It diverges when,
thus,
WHich is impossible.
It is inconclusive when, ,
Thus, .
But we can this that this series is convergent abolsutely thus, this is absolutely convergenet everywhere.