P Series

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Intros
Lessons
  1. P series Overview
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Examples
Lessons
  1. Convergence and Divergence of P Series
    Determine whether the series is convergent or divergent
    1. ∑n=3∞1n2 \sum_{n=3}^{\infty}\frac{1}{n^2}
    2. ∑n=1∞n3+1n2 \sum_{n=1}^{\infty}\frac{n^3+1}{n^2}
  2. For what values of kk does the series ∑n=1∞n3+1n(2k+1)\sum_{n=1}^{\infty}\frac{n^3+1}{n^{(2k+1)}} converge and diverge?
    Topic Notes
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    In this lesson, we will learn about p-series. They take on a special form, and look very similar to Harmonic series. However their convergence or divergence depends on the denominator's exponent, p. If p is greater than 1, then the series converge. If p is less than 1, then the series diverge. In this lesson, we will start off with looking at some simple p-series questions. Then we will look at a complicated p-series which convergences and divergences depending on a certain value.
    Note *P Series are in the form:
    ∑n=1∞1np \sum_{n=1}^{\infty}\frac{1}{n^p}
    where if pp > 1 then the series converge. Otherwise, the series diverges.
    Basic Concepts
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