Understand infinite series, convergence, and divergence with interactive visualizations and step-by-step examples.
📘 Start Learning SeriesAn infinite series is the sum of all terms in a sequence. They appear in physics, engineering, and mathematics for modeling complex patterns.
a₁ + a₂ + a₃ + ... = ∑ aₙ from n=1 to ∞
An example: The sum of 1 + 1/2 + 1/4 + 1/8 + ... converges to 2
Interactive series convergence visualization
Σ rⁿ converges when |r| < 1. Used to model repeating decimals and exponential decay.
Σ 1/n diverges. Surprisingly, the sum grows without bound as n increases.
Σ 1/nᴾ converges if p > 1, diverges if p ≤ 1.
Limit as n→∞ of |aₙ₊₁/aₙ|
Converges if limit < 1, diverges if > 1.
Compare series to an integral of function f(x).
Σ aₙ converges if integral of f(x) from 1 to ∞ converges.
What is the sum of this geometric series? Σ (1/5)*2ⁿ for n=0 to ∞
Take quizzes, watch step-by-step solutions, and solve real-world problems.