Question

If [infinity]∑n=0cn9n is convergent, does it follow that the following series are convergent? (a) [infinity]∑n=0cn(−3)n

Answer 1

Given: The series ∑cₙ
`9^n` is convergent

To find: The series ∑cₙ
`(-3)^n` is convergent or not.

Solution: If the radius of convergence R the we can conclude that R≥4

So, the series will converge as -3<9.