755 prompts matching "Why the sum to infinity fails when the ratio reaches one"
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Applying the sum to infinity formula when the ratio lies between minus one and one
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Show All Working: The sum to infinity of a geometric progression, and when it exists
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Explaining why sum to infinity only works for |r| < 1
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Common Mistakes: Rationalising when both terms of the denominator are surds
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Worked Example: Which form of the sum formula to use when r is less than one
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Rationalising the denominator when it's a surd minus a surd
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Spot My Mistake: The decimal expansion of an irrational number, and why it never repeats
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Final Revision: Why brackets matter when an operation is not associative
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Explaining why we rationalise denominators
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Worked Example: Why the square root of a non-square whole number is irrational
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Common Mistakes: Why a rational number added to an irrational one stays irrational
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Quiz: Rationalising a denominator of the form one over root 3
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Spot My Mistake: Rationalising and then cancelling a common factor
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Quiz: Rationalising a denominator of the form one over 2 plus root 3
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Final Revision: Why distributivity links two operations rather than one
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Practice: Finding n when the sum of an arithmetic progression is given
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Spot My Mistake: Finding the common ratio when the third and sixth terms are given
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Practice: Finding n when the sum of a geometric progression is given
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Explain Back: The sum of a geometric progression with a negative common ratio
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Factorising the sum and difference of two cubes
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