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Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

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That's that last lesson.

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Get Started Now- Lesson: 11:08
- Lesson: 2a6:09
- Lesson: 2b4:40
- Lesson: 323:42

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:

$\sum_{n=1}^{\infty}\frac{1}{n^p}$

where if $p$ > 1 then the series converge. Otherwise, the series diverges.

$\sum_{n=1}^{\infty}\frac{1}{n^p}$

where if $p$ > 1 then the series converge. Otherwise, the series diverges.

- 1.P series Overview
- 2.
**Convergence and Divergence of P Series**

Determine whether the series is convergent or divergenta)$\sum_{n=3}^{\infty}\frac{1}{n^2}$b)$\sum_{n=1}^{\infty}\frac{n^3+1}{n^2}$ - 3.For what values of $k$ does the series $\sum_{n=1}^{\infty}\frac{n^3+1}{n^{(2k+1)}}$ converge and diverge?

5.

Sequence and Series

5.1

Introduction to sequences

5.2

Monotonic and bounded sequences

5.3

Introduction to infinite series

5.4

Convergence and divergence of normal infinite series

5.5

Convergence & divergence of geometric series

5.6

Convergence & divergence of telescoping series

5.7

Divergence of harmonic series

5.8

P Series

5.9

Alternating series test

5.10

Divergence test

5.11

Comparison & limit comparison test

5.12

Integral test

5.13

Ratio test

5.14

Root test

5.15

Absolute & conditional convergence

5.16

Radius and interval of convergence with power series

5.17

Functions expressed as power series

5.18

Taylor series and Maclaurin series

5.19

Approximating functions with Taylor polynomials and error bounds

We have over 170 practice questions in Integral Calculus for you to master.

Get Started Now5.1

Introduction to sequences

5.2

Monotonic and bounded sequences

5.4

Convergence and divergence of normal infinite series

5.5

Convergence & divergence of geometric series

5.6

Convergence & divergence of telescoping series

5.7

Divergence of harmonic series

5.8

P Series

5.9

Alternating series test

5.10

Divergence test

5.11

Comparison & limit comparison test

5.12

Integral test

5.13

Ratio test

5.14

Root test

5.15

Absolute & conditional convergence

5.16

Radius and interval of convergence with power series

5.17

Functions expressed as power series

5.18

Taylor series and Maclaurin series