Question

Which of the following series are convergent?

i. sum 12^n

ii. sum 1n

iii. sum (-1)^n3n-1

a) i only

b) ii only

c) iii only

d) i and iii

Answer 1

The convergent series are i. sum 12^n and iii. sum (-1)^n3n-1.

Step-by-step explanation:

The series that are convergent are:

1. i. sum 12^n (convergent)
2. iii. sum (-1)^n3n-1 (convergent)

i. sum 12^n is convergent because as n approaches infinity, the terms of the series become increasingly large and the series diverges.

iii. sum (-1)^n3n-1 is also convergent because as n approaches infinity, the terms of the series become increasingly small and the series alternates between positive and negative values, resulting in a convergent series.