Geometric Sequences & Series (Edexcel A-Level Mathematics): Quizzes

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Geometric Series
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What term describes a series where the sum grows without bound as more terms are added?

Diverges

What happens to the series 12+14+18+116+\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \frac{1}{16} + \ldots as nn \to \infty?

Sn1S_n \to 1 (converges)

What is the condition for a geometric series to converge?

r<1|r| < 1

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

S=a1rS_{\infty} = \frac{a}{1-r}

If r<1|r| < 1, what happens to rnr^n as nn \to \infty?

rn0r^n \to 0

Does the series 6+2+23+29+6 + 2 + \frac{2}{3} + \frac{2}{9} + \ldots converge or diverge?

Converges

Find the sum to infinity of 6+2+23+29+6 + 2 + \frac{2}{3} + \frac{2}{9} + \ldots

99

Which common ratio would cause the series 1+2+4+8+1 + 2 + 4 + 8 + \ldots to diverge?

r=2r = 2

If sum to infinity equals 4 times the first term, what is rr?

34\frac{3}{4}

If r=34r = \frac{3}{4} and the third term is 99, find aa.

1616

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