// Numbas version: exam_results_page_options
{"name": "Simon's copy of  Binomial series for non-Natural exponent", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "<p>The binomial series expansion for an expression of the form \\((1+bx)^{n}\\) where \\(n\\) is a non-natural number, is given by:</p>\n<p style=\"padding-left: 30px;\">\\((1+bx)^{n}=1+n(bx)^{1}+\\frac{n(n-1)}{2!}(bx)^{2}+\\frac{n(n-1)(n-2)}{3!}(bx)^{3}+...\\)</p>\n<p>In this example &nbsp;\\(n=\\frac{1}{\\var{n}}\\), &nbsp; and &nbsp;\\(b=\\var{b}\\).</p>\n<p>So the&nbsp;first three terms are</p>\n<p style=\"padding-left: 30px;\">\\((1+\\var{b}x)^{\\frac{1}{\\var{n}}}=1+{\\frac{1}{\\var{n}}}(\\var{b}x)^{1}+\\frac{{\\frac{1}{\\var{n}}}\\times (\\frac{1}{\\var{n}}-1)}{2!}(\\var{b}x)^{2}\\)</p>\n<p style=\"padding-left: 30px;\">\\((1+\\var{b}x)^{\\frac{1}{\\var{n}}}\\)= $ \\simplify[all,!collectNumbers]{{T1}+{T2}x+{T3}x^2}$</p>", "parts": [{"showCorrectAnswer": true, "showPreview": true, "checkingType": "absdiff", "variableReplacements": [], "checkVariableNames": false, "customMarkingAlgorithm": "", "scripts": {}, "prompt": "<p>Input the first three tems in&nbsp;the binomial series expansion.&nbsp;</p>", "type": "jme", "answer": "{T1}+{T2}x+{T3}x^2", "vsetRange": [0, 1], "expectedVariableNames": [], "extendBaseMarkingAlgorithm": true, "unitTests": [], "checkingAccuracy": 0.001, "showFeedbackIcon": true, "failureRate": 1, "variableReplacementStrategy": "originalfirst", "answerSimplification": "all,!collectNumbers", "vsetRangePoints": 5, "marks": "3"}], "variables": {"T3": {"templateType": "anything", "description": "", "definition": "{b}^2*(1/{n}*(1/{n}-1))/2", "group": "Ungrouped variables", "name": "T3"}, "T2": {"templateType": "anything", "description": "", "definition": "{b}/{n}", "group": "Ungrouped variables", "name": "T2"}, "b": {"templateType": "randrange", "description": "", "definition": "random(2..12#1)", "group": "Ungrouped variables", "name": "b"}, "n": {"templateType": "randrange", "description": "", "definition": "random(2..6#1)", "group": "Ungrouped variables", "name": "n"}, "T1": {"templateType": "anything", "description": "", "definition": "1", "group": "Ungrouped variables", "name": "T1"}}, "tags": [], "statement": "<p>Given the expression \\((1+\\var{b}x)^{\\frac{1}{\\var{n}}}\\)</p>", "ungrouped_variables": ["b", "n", "T1", "T2", "T3"], "preamble": {"js": "", "css": ""}, "name": "Simon's copy of  Binomial series for non-Natural exponent", "extensions": [], "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "functions": {}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": "<p>Find the first three terms in the binomial series expansion having a non-Natural exponent</p>"}, "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}