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[tex]\Sigma_{n=1}^{ \infty} \frac{1}{(3n-2)(3n+1)} [/tex] I simplified it to partial fractions to (1/3) / (3n-2) - (1/3) / (3n+1) Now what?
An infinite series is a mathematical expression that represents the sum of an infinite number of terms. It can be written in the form of a1 + a2 + a3 + ... + an + ..., where a1, a2, a3, etc. are the terms of the series and n is the number of terms.
Partial fractions are a way to break down a complex fraction into smaller, simpler fractions. This technique is often used to simplify mathematical expressions involving rational functions.
Infinite series can often be written as a ratio of polynomials, which can then be broken down into partial fractions. This simplifies the series by breaking it down into smaller, more manageable parts.
The process involves breaking down the series into a ratio of polynomials, then finding the partial fractions for each individual polynomial. These partial fractions are then combined to form a simpler expression.
Yes, there are limitations. Partial fractions can only be used on series that can be written as a ratio of polynomials. They also cannot be used on series with non-rational functions, such as trigonometric functions.