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3 years ago

Which expression is a irrational number? A. 0.78 repeating

Mathematics

2 answers:

katen-ka-za [31]3 years ago

6 0

Answer:

The answer is C. Square root √18

Step-by-step explanation:

you are looking for irrational number.

if use a calculator and you see that the √18 is 4.242642687119285 is a non-terminated number and non-repeated number so its irrational

the other three is rational because you can turn them into a fraction and we don't want that.

Oxana [17]3 years ago

4 0

An irrational number has an infinite decimal expansion that does not repeat. Numbers that have infinite decimal expansions that do not repeat cannot be expressed as the fraction of two integers.

A rational number is any number that can be expressed as the fraction of two integers.

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Answer:

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Step-by-step explanation:

Geometric sequence

General form of a geometric sequence: $a_n=ar^{n-1}$

(where a is the first term and r is the common ratio)

Given:

$\displaystyle \sum^{20}_{n=1} 4 \left(\dfrac{8}{9}\right)^{n-1}$

Therefore:

a = 4
r = 8/9

Sum of the first n terms of a geometric series:

$S_n=\dfrac{a(1-r^n)}{1-r}$

To find the sum of the first 20 terms, substitute the found values of a and r, together with n = 20, into the formula:

$\implies S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}$

$\implies S_{20}=32.58609013...$

$\implies S_{20}=32.59\:\: \sf (nearest\:hundredth)$

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