Infinite Series (Leaving Cert Mathematics): Flashcards

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Infinite Series
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9 cards from this deck

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Effect of incremental terms in geometric series

Contribute less to total sum as nn increases

Condition for geometric series convergence

∣r∣<1|r| < 1

Formula for sum to infinity of geometric series

S∞=a1−rS_\infty = \frac{a}{1-r}

What is a recurring decimal?

Digit repeats to infinity

Notation for recurring decimal

Dot on top of repeating digit(s)

Method to convert recurring decimal to fraction

Use sum to infinity on repeating part

S∞S_\infty for sequence 16,8,4,2,...16, 8, 4, 2, ...

3232

What series forms in the repeating part of a recurring decimal?

Geometric series to infinity

0.12˙0.1\dot{2} expressed as a fraction

1190\frac{11}{90}

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