Infinite Series & Cubic Sequences (Leaving Cert Mathematics): Quizzes

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Infinite Series
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What is the common ratio in the sequence 1,12,14,18,...1, \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, ...?

12\frac{1}{2}

As more terms are added in a convergent geometric series, what happens to each term's contribution?

It contributes less to the total sum

For what values of rr does a geometric series have a sum to infinity?

r<1|r| < 1

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

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

For the sequence 16,8,4,2,...16, 8, 4, 2, ..., what is the sum to infinity?

3232

What does the notation 0.12˙0.1\dot{2} represent?

0.1222222...0.1222222...

What is S5S_5 in the series 1+12+14+18+...1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...?

1.93751.9375

In converting 0.12˙0.1\dot{2} to a fraction, what is the first term aa of the repeating geometric series?

2100\frac{2}{100}

What is the common ratio rr for the geometric series in the repeating part of 0.12˙0.1\dot{2}?

110\frac{1}{10}

What fraction is equivalent to 0.12˙0.1\dot{2}?

1190\frac{11}{90}

What does the notation 4.2˙3˙4.\dot{2}\dot{3} represent?

4.232323...4.232323...

In the example, what value does the series approach as nn increases to infinity?

It converges to some value

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