The Formula for Taylor Series | Summary and Q&A

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January 3, 2019
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The Formula for Taylor Series

TL;DR

Adding fractions with polynomials is easier when converting them to decimal form or using the Taylor series.

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Questions & Answers

Q: Why is adding fractions challenging?

Adding fractions can be difficult because the denominators may be different, requiring the use of a common denominator. Additionally, when dealing with fractions in decimal form, the numbers can be complicated, making addition more challenging.

Q: How can converting fractions to decimals make addition easier?

Converting fractions to decimals eliminates the need for finding a common denominator. It allows for adding the numbers term by term, similar to adding numbers in the place value system.

Q: What are the advantages of converting functions to polynomials?

Converting functions like e^x and 1/(1-x) to polynomials makes addition easier because polynomials can be added term by term. This simplifies the process and allows for finding the sum of the functions.

Q: What is the Taylor series?

The Taylor series is a power series that represents a function as an infinite polynomial. It can be used to approximate a complicated function by finding its coefficients and center. The Taylor series is a useful tool in calculus.

Summary & Key Takeaways

  • Adding fractions can be challenging, but it becomes simpler when converting them to decimal form and adding them term by term.

  • Adding functions like e^x and 1/(1-x) is difficult, but converting them to polynomials allows for easier addition.

  • The power series, known as the Taylor series, can be used to write a complicated function as an infinite polynomial.

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