Sequences and Series

Front

nth Term of a Geometric Sequence

Back

Given by: a_n = a₁ r^n-1, where a₁ is the first term and r is the common ratio.
Or a_n = a₀rⁿ
Or a_n = a₂ r^n-2

10.2

Front

Geometric Infinite Series Convergence

Back

Front

Geometric Infinite Series Divergence

Back

A geometric series diverges if |r| ≥ 1.

10.2

Front

Nth Term Test for Divergence

Back

Front

Integral Test for Convergence

Back

Front

P-Series Convergence

Back

Front

Harmonic Series

Back

Front

Comparison Test for Convergence

Back

Compare to a known series:

If 0 ≤ aₙ ≤ bₙ and ∑bₙ converges, then ∑aₙ converges.

If aₙ ≥ bₙ ≥ 0 and ∑bₙ diverges, then ∑aₙ diverges.

10.6

Front

Limit Comparison Test

Back

Front

Alternating Series Test for Convergence

Back

If terms alternate in sign, decrease in magnitude, and approach 0, the series converges.

10.7