Calculus II · Unit 4A · reference
Common Errors in Sequence and Series Problems
Common Errors in Sequence and Series Problems
Do not confuse necessary with sufficient
The condition is necessary for to converge, but it is not sufficient.
Do not compare in the useless direction
Being smaller than a divergent series proves nothing; being larger than a convergent series proves nothing.
Do not forget endpoint tests
A power-series radius settles the open interval only. Endpoints are separate series problems.
After the explanation
Use the section idea
Mixed work removes the method label; classify first, complete an honest attempt, then diagnose the earliest incorrect decision.
A complete series argument includes hypotheses, a named theorem or comparison, its conclusion, and any requested sum or error estimate.
Identify the object and structure before computing, then use answer reveals only after recording a complete justification.
Reading the key before choosing a test or treating a missing hypothesis as a minor presentation issue.
Can you reproduce the argument without the key and explain why a tempting alternative test is weaker?
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