Question

if the power series ∑n=1 ∞​ a n x^n converges uniformly in ]alpha,beta[,then so does∑n=0 ∞ an(-x^n) true or false ?justify​

Answer 1

Answer:

Since x^n is positive, monotonic decreasing and bounded for -1<= x<=1, and the series summation infinity,n=0 anx^n is uniformly convergent, therefore the given series also converges in-1<=x<=1.

True.