If the series Cnx^n converges when x=-3 and diverges when x=4, which of the series converge

A. (-1)^n Cn9^n
B. Cn
C. Cn(-3)^(n+1)

It can be more than one choice :)

By hypothesis, the radius of convergence for Σc(n) x^n is at least |-3| = 3, and no bigger than 4 (since x = -4 could potentially yield convergence, if R is indeed 4).

Hence, A diverges (since |-9| = 9 > 4), while B and C converge (since |1|, |-3| ≤ 3.)

I hope this helps!