Question

suppose that sigma (cnx^(n)) converges when x=-5 and diverges when x=8. would sigma cn diverge or converge and also would sigma cn2^(n) diverge or converge

Answer 1

If a power series
\[ \sum_1^\infty c_n x^n\]
converges for a number x., the it converges absolutely for x < a.
for x=1 it converges and for x=2 it converges.

Answer 2

The x should be a.
converges for a number a.,
then it converges absolutely for x < a. for x=1 it converges and for x=2 it converges.

Answer 3

Since 1 and 2 are less than |-5|=5