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\n \n \n ", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "marks": 0}], "variables": {"t_statements": {"templateType": "list of strings", "group": "Statements", "definition": "[ \"A convergent sequence is bounded.\", \"An unbounded sequence does not converge.\", \"It is possible for a sequence to be both increasing and decreasing.\", \"A sequence with only a finite number of non zero terms converges to 0.\", \"A bounded increasing sequence converges.\", \"A bounded decreasing sequence converges.\", \"There are convergent sequences with all terms greater than zero and the limit is 0.\" ]", "name": "t_statements", "description": ""}, "f_statements": {"templateType": "list of strings", "group": "Statements", "definition": "[ \"A bounded sequence is convergent.\", \"Every divergent sequence is unbounded.\", \"Every convergent sequence is monotone.\", \"There are convergent sequences with all terms greater than zero and the limit is less than zero.\", \"There are bounded monotone sequences that do not converge.\", \"All convergent sequences of positive terms converge to a value greater than zero.\", \"There are unbounded sequences which converge.\", \"It is not possible for a sequence to be both increasing and decreasing.\" ]", "name": "f_statements", "description": ""}, "choices": {"templateType": "anything", "group": "Statements", "definition": "shuffle(0..len(statements)-1)[0..6]", "name": "choices", "description": ""}, "statements": {"templateType": "anything", "group": "Statements", "definition": "t_statements+f_statements", "name": "statements", "description": ""}, "statement_marks": {"templateType": "anything", "group": "Statements", "definition": "map([1,-1],x,t_statements)+map([-1,1],x,f_statements)", "name": "statement_marks", "description": ""}}, "ungrouped_variables": [], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "name": "True/false statements about limits of sequences", "functions": {}, "variable_groups": [{"variables": ["t_statements", "f_statements", "statements", "statement_marks", "choices"], "name": "Statements"}], "showQuestionGroupNames": false, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "\n \n \n

Answer the following question on limits of sequences. Note that a sequence is unbounded if it is not bounded.

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Note that every correct answer is worth 1 mark – but every wrong answer loses a mark.

\n \n \n ", "tags": ["bounded sequences", "checked2015", "convergence", "convergent sequences", "decreasing sequence", "divergence", "divergent sequences", "increasing sequence", "limits", "mas1601", "MAS1601", "monotone sequence", "monotonic sequence", "sequence", "sequences", "subsequence", "tested1", "unbounded sequences"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "

5/07/2012:

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Added tags.

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21/07/2012:

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Added description.

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27/7/2012:

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Added tags.

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 24/12/2012:

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Checked choices, OK. Added tested1 tag.

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Also included escaped slashes in string variables including tex.

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Multiple response question (3 correct out of 6) re properties of convergent and divergent sequences. Selection of questions from a pool.

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Check against your course notes.

\n \n \n ", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}