convergence

A Cauchy sequence is a special type of sequence where, as you move further along, the terms get closer and closer to each other.

The superior and inferior limits of a sequence describe the largest and smallest values around which the terms continue to accumulate asymptotically.

A series is the limit of the sum of the terms of a sequence. It may converge, diverge, or be indeterminate.

A geometric series is a sum of terms where each term is obtained by multiplying the previous one by a constant ratio. Its convergence depends on the value of the ratio.

A telescoping series is a series whose terms cancel successively when added, causing the partial sums to collapse to a small number of surviving terms.

A Taylor series is a representation of a function as an infinite sum of polynomial terms determined by its derivatives at a single point. It provides a fundamental tool for approximating functions, studying convergence, and understanding analytic behaviour in real analysis.

A Fourier series represents a periodic function as an infinite sum of sine and cosine functions.