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Orlov [11]
3 years ago
6

Evaluate the infinite geometric series 0.79 + 0.079 + 0.0079 + 0.00079 + 0.000079. Express your answer as a fraction with intege

r numerator and denominator.
Mathematics
1 answer:
tamaranim1 [39]3 years ago
3 0

Answer:

The fraction is 79/99

Step-by-step explanation:

We can express the given infinite geometric series as follows:

\frac{79}{10^{2} }+\frac{79}{10^{3} }+\frac{79}{79^{4} }+\frac{79}{10^{5} }+...

Which is an infinite geometric series with r=\frac{1}{10^{2} } that converges, then its sum is:

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

Where a is the first factor of the serie: a=\frac{79}{10^{2} }

Replacing values:

S=\frac{\frac{79}{10^{2} } }{1-\frac{1}{10^{2} } }  \\S=\frac{\frac{79}{10^{2} } }{\frac{99}{10^{2} } }\\S=\frac{79}{99}

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