When a series or sequence diverges, it means that the terms of the series or sequence do not approach a finite value as the number of terms increases. In other words, the sum or limit of the terms does not exist.
Imagine you're trying to catch a train that keeps moving further away from you. No matter how fast you run, you can never reach it because it's always getting farther and farther away. Similarly, when a series or sequence diverges, no matter how many terms you add up or how far along in the sequence you go, you'll never reach a final sum or limit.
Converges: When a series or sequence converges, it means that the terms of the series or sequence approach a finite value as the number of terms increases. The sum or limit exists.
Infinite Series: An infinite series is an expression consisting of an infinite number of terms added together.
Geometric Series: A geometric series is a specific type of infinite series where each term is obtained by multiplying the previous term by a constant ratio.
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