Question

Test the series for convergence or divergence:

∑
k=1
[infinity]
​
(x−1)(k+4)
3
. What is the answer?
a) Converges
b) Diverges
c) Cannot be determined from the given information
d) Convergence depends on the value of x

Answer 1

The convergence of the series ∑ (x-1)(k+4)^3 depends on the value of x. It converges if x = 1 and diverges for any other value of x.

Step-by-step explanation:

The series in question is of the form ∑ (x-1)(k+4)^3. Without knowing the value of x, we cannot test the series for convergence or divergence. The convergence of this series depends on the value of x. If x equals 1, the series converges to 0 as each term of the series will be zero. If x does not equal 1, the series will diverge because the terms do not approach zero as k goes to infinity. Thus, the answer is (d) Convergence depends on the value of x.