All You Need in One Place

Everything you need for better marks in primary, GCSE, and A-level classes.

Learn with Confidence

We’ve mastered the UK’s national curriculum so you can study with confidence.

Instant and Unlimited Help

24/7 access to the best tips, walkthroughs, and practice questions.

0/1
?
Intros
Lessons
  1. P series Overview
0/3
?
Examples
Lessons
  1. Convergence and Divergence of P Series
    Determine whether the series is convergent or divergent
    1. n=31n2 \sum_{n=3}^{\infty}\frac{1}{n^2}
    2. n=1n3+1n2 \sum_{n=1}^{\infty}\frac{n^3+1}{n^2}
  2. For what values of kk does the series n=1n3+1n(2k+1)\sum_{n=1}^{\infty}\frac{n^3+1}{n^{(2k+1)}} converge and diverge?
    Topic Notes
    ?
    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=11np \sum_{n=1}^{\infty}\frac{1}{n^p}
    where if pp > 1 then the series converge. Otherwise, the series diverges.