Domanda del libro di testo
Write out the first three terms and the last term. Then use the formula for the sum of the first n terms of an arithmetic sequence to find the indicated sum.
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Ch. 8 - Sequences, Induction, and Probability
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 9, Problema 45
Express each repeating decimal as a fraction in lowest terms.
Guida verificata passo dopo passo1
Let the repeating decimal be represented by the variable \(x\), so \(x = 0.5555\ldots\) where the digit 5 repeats indefinitely.
Multiply both sides of the equation by 10 to shift the decimal point one place to the right: \(10x = 5.5555\ldots\)
Subtract the original equation from this new equation to eliminate the repeating part: \(10x - x = 5.5555\ldots - 0.5555\ldots\)
Simplify the subtraction: \(9x = 5\)
Solve for \(x\) by dividing both sides by 9: \(x = \frac{5}{9}\). This fraction is already in lowest terms.
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Repeating Decimals
A repeating decimal is a decimal number in which a digit or group of digits repeats infinitely. For example, 0.555... has the digit 5 repeating endlessly. Understanding this pattern is essential to convert such decimals into fractions.
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How to Graph Rational Functions
Geometric Series
A geometric series is the sum of terms where each term is a constant multiple (common ratio) of the previous one. In repeating decimals, the infinite sum of the repeating digits can be expressed as a geometric series, which helps in finding the fractional equivalent.
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4:18Geometric Sequences - Recursive Formula
Fraction Simplification
After expressing the repeating decimal as a fraction, simplifying it to lowest terms involves dividing numerator and denominator by their greatest common divisor (GCD). This ensures the fraction is in its simplest and most understandable form.
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05:45Radical Expressions with Fractions
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