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Sequences & series intro

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Sequences introWorked example: sequence explicit formulaWorked example: sequence recursive formulaGeometric sequence reviewExtending geometric sequencesUsing explicit formulas of geometric sequencesUsing recursive formulas of geometric sequences
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Convergent and divergent sequencesWorked example: sequence convergence/divergenceFormal definition for limit of a sequenceProving a sequence converges using the formal definition
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Summation notationConverting explicit series terms to summation notationConverting explicit series terms to summation notation (n ≥ 2)Arithmetic series formulaWorked example: arithmetic series (sigma notation)Worked example: arithmetic series (sum expression)Worked example: arithmetic series (recursive formula)
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Geometric series introGeometric series with sigma notationWorked example: finite geometric series (sigma notation)Worked examples: finite geometric seriesFinite geometric series formula
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Partial sums introPartial sums: formula for nth term from partial sumPartial sums: term value from partial sumInfinite series as limit of partial sums
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Worked example: convergent geometric seriesWorked example: divergent geometric seriesInfinite geometric series formula intuitionProof of infinite geometric series as a limitInfinite geometric series word problem: bouncing ballInfinite geometric series word problem: repeating decimalConvergent & divergent geometric series (with manipulation)
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Telescoping seriesDivergent telescoping seriesSum of n squares (part 1)Sum of n squares (part 2)Sum of n squares (part 3)Evaluating series using the formula for the sum of n squares

About this unit

Sequences are like chains of ordered terms. Series are sums of terms in sequences. These simple innovations uncover a world of fascinating functions and behavior.