// 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}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "

The binomial series expansion for an expression of the form \$$(1+bx)^{n}\$$ where \$$n\$$ is a non-natural number, is given by:

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\$$(1+bx)^{n}=1+n(bx)^{1}+\\frac{n(n-1)}{2!}(bx)^{2}+\\frac{n(n-1)(n-2)}{3!}(bx)^{3}+...\$$

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In this example  \$$n=\\frac{1}{\\var{n}}\$$,   and  \$$b=\\var{b}\$$.

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So the first three terms are

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\$$(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}\$$

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\$$(1+\\var{b}x)^{\\frac{1}{\\var{n}}}\$$= $\\simplify[all,!collectNumbers]{{T1}+{T2}x+{T3}x^2}$

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Input the first three tems in the binomial series expansion.

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Given the expression \$$(1+\\var{b}x)^{\\frac{1}{\\var{n}}}\$$

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Find the first three terms in the binomial series expansion having a non-Natural exponent

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