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[null,"Binomial Expansion"]
[]
[null,"This tool calculates up to the x¹⁰ term of a binomial expansion, "]
[null,"and can accept both negative and fractional powers as well as natural numbers.  "]
[]
[null,"Coefficients are given to 4 decimal places where appropriate.  "]
[]
[null,"Where the expansion is infinite, or contains more terms than calculated, ... Is shown after the final term calculated.  "]
[]
[null,"The calculator contains a macro which activates the approximation function.  "]
[null,null,"The approximation function allows you to set a value for x and calculate, one term at a time (using the arrows),"]
[null,null,"a progressive approximation for the value of the expansion.  "]
[null,null,"The 'true' value (Excel's direct calculation) is shown alongside"]
[]
[null,"The graph (which is shown when the Approximation feature is active) indicates the value of the approximation at each"]
[null,"level of detail progressively, demonstrating the nature of convergent, divergent, oscillating and terminating sequences.  "]
[]
[null,"The sheet is protected to avoid accidentally deleting formulae, etc.  "]
[null,"To unprotect, right click on the sheet tab and select Unprotect Sheet.  There is no password.  "]
[]
[null,"Note:","If clicking the appropriate arrow doesn't show more terms when it should (the graph will also not respond)"]
[null,null,"it is because the level of accuracy for calculations is not precise enough - increasing the number of decimal places"]
[null,null,"will fix this.  "]
[]
[null,"Note:","Some binomial expansions converge, but relatively slowly.  For instance, (1+2x)-3 passes the test for convergence, "]
[null,null,"but this may not be apparent from the graph depending on the value of x chosen.  "]
[null,null,"It may be useful to note this, and observe what changes result in rapid convergence.  "]
[null,null,"In Approximation mode, a cell will return \"Converges\" or \"Does not converge\" for when the graph is unclear.  "]

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["Binomial Expansion"]
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