Math Problem Solver

Q1 (6 marks) – Alternating Series Test and nth-term limit

Consider the alternating series

∑

n

=

1

∞

(

−

1

)

n

+

1

1

n

.

n=1

∑

∞

​

(−1)

n+1

n

1

​

.

State the Alternating Series Test. (2)

Show that the given series satisfies the hypotheses of the Alternating Series Test, and hence converges. (2)

Explain why the series

∑

n

=

1

∞

∣

(

−

1

)

n

+

1

n

∣

n=1

∑

∞

​

​

n

(−1)

n+1

​

​

diverges, and classify the original series as absolutely or conditionally convergent. (2)