Determine whether the sequence converges or diverges. If it converges, give the limit.
1 answer:
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Answer:
= Irrational
43.95 (repeat sign) = Rational
-3π = Irrational
-√49 = Rational
6/15 = Rational
Step-by-step explanation:
Note:
A rational number can be defined as any number that can be expressed or written in the p/q form, where 'p' and 'q' are integers and q is a non-zero number. An irrational number on the other hand cannot be expressed in p/q form and the decimal expansion of an irrational number is non-repeating and non-terminating.
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The square root of a negative number is imaginary.
Natural Number Test
A number is natural if it is one of the counting numbers (greater than 0), i.e., 1,2,3,4,5,...
Since NAN is not both positive and a counting number, NAN is not a natural number
Whole Number Test:
Whole Numbers are positive numbers, including 0, with no decimal or fractional parts
Since NAN is not both ≥ 0 and an integer, NAN is a not a whole number
Integer Test
The number is an integer if it is a whole number (no fractions or decimals) positive or negative including the number 0, ...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...
Since NAN is not a positive or negative number (no decimals or fractions), NAN is not an integer
Rational Number Test
The number NAN is rational if it is an integer or decimal
A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.
Irrational Number Test:
An irrational number is a number that cannot be expressed as a ratio between two integers and is not an imaginary number.
Since NAN is the square root of a negative number, it is imaginary
Imaginary Numbers are not rational
Imaginary
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43.95 ⇒ With repeat sign over 43.95
The decimal places repeat an infinite amount of times and when a decimal repeats it's rational.
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Pi is a Greek letter (π), and one of the most well-known mathematical constants.
It is the ratio of a circle's circumference to its diameter which is always constant.
pi (π) approximately equals 3.14159265359... and is a non-terminating non-repeating decimal number.
Hence 'pi' is an irrational number.
Any number with pi is considered irrational.
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The square root of a negative number is imaginary.
Natural Number Test
A number is natural if it is one of the counting numbers (greater than 0), i.e., 1,2,3,4,5,...
Since NAN is not both positive and a counting number, NAN is not a natural number
Whole Number Test:
Whole Numbers are positive numbers, including 0, with no decimal or fractional parts
Since NAN is not both ≥ 0 and an integer, NAN is a not a whole number
Integer Test
The number is an integer if it is a whole number (no fractions or decimals) positive or negative including the number 0, ...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...
Since NAN is not a positive or negative number (no decimals or fractions), NAN is not an integer
Rational Number Test
The number NAN is rational if it is an integer or decimal
A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0.
Irrational Number Test:
An irrational number is a number that cannot be expressed as a ratio between two integers and is not an imaginary number.
Since NAN is the square root of a negative number, it is imaginary
Imaginary Numbers are not rational
Imaginary
But is rational as it equals -7.
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Rational because the decimal terminates:
6/15 = 0.4/0.40...
