AP Calculus BC Unit 10 Named Series'

What is a geometric series?

A geometric series is of the form \sum_{n=0}^{\infty} ar^n where a is the first term and r is the common ratio. It converges if |r| < 1 and diverges if |r| \geq 1.

What is the harmonic series?

The harmonic series is represented as: H_n = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + … + \frac{1}{n} as n approaches infinity. This series diverges.

What is a p-series?

A p-series is of the form \sum_{n=1}^{\infty} \frac{1}{n^p}. This series converges if p > 1 and diverges if 0 < p \leq 1.

Sigma

Sigma