MATH1120 Lecture Notes - Lecture 1: Taylor Series
10 Oct 2018
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Defined as: t1, t1 + t2, t1 + t2 + t3 known as the sequence of partial sums for the series. Convergence: when the sum of the infinite series approaches a certain number, or when the sum reaches a certain value and does not change. Divergence: any other behaviour where the sum does not approach a certain value. Tests that can be applied to determine if a series converges or diverges include: Power series have particular qualities that differentiate them from other series, they will either: converge only for x = a, converge for |x a| < r and diverge for |x a| > r. |x a| < r is defined as the interval of convergence of the power series. The value r is defined as the radius of convergence: converge for all values of x. An infinite series representation for a given function of one variable.
