Infinite Series (Grade 12 NSC Matric Mathematics): Quizzes

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Infinite Series
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What can happen when adding infinitely many terms together?

The sum can approach a finite value

What defines a convergent series?

Sum approaches a certain value; has limit

For which values of rr does a geometric series converge?

−1<r<1-1 < r < 1

What is the sum to infinity formula for a convergent geometric series?

S∞=a1−rS_{\infty} = \frac{a}{1-r}

Find S∞S_{\infty} for the series 18+6+2+...18 + 6 + 2 + ...

2727

Does a geometric series with r=2r = 2 converge?

No, it diverges

Do arithmetic series converge?

Never; they tend to ±∞\pm\infty

What is 0.5‾0.\overline{5} as a fraction using infinite series?

59\frac{5}{9}

What is the common ratio for series 18+6+2+...18 + 6 + 2 + ...?

13\frac{1}{3}

What happens to rnr^n as nn approaches infinity in a convergent series?

rnr^n approaches 00

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