For the series $$\(\sum_{n=1}^{\infty}\)$$, if $$\((-1)^{n+1} \cdot \frac{1}{n^{2}}\)$$, the truncation error after the fifth term will be less than $$\(\frac{1}{36}\)$$ because I. the terms alternate signs. II. the terms decrease in absolute value. III. the terms approach 0 as a limit.

A.
I only
B.
I and II only
C.
II and III only
D.
I, II, and III are true and required.
Calculus
AP
College Board
Exam No:AP Calculus Unit 10 Questions Set 2 Year:2024 Question No:23

Answer:

D

Knowledge points:

10.10 Alternating Series Error Bound
10.7 Alternating Series Test for Convergence

Solution:

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