Definition of a Sequence: A sequence is a sequence of numbers that follows a specific pattern or rule. Each term in the sequence is obtained by applying a d...
Definition of a Sequence:
A sequence is a sequence of numbers that follows a specific pattern or rule. Each term in the sequence is obtained by applying a defined function to the preceding term(s).
Convergence of Sequences:
A sequence converges to a single real number as the number of terms approaches infinity. This means that the sequence approaches that specific number as the count of terms increases without bound.
Examples:
The sequence {1, 2, 3, 4, 5} converges to 5 as the number of terms approaches infinity.
The sequence {0, 1, 2, 3, 4} converges to 3 as the number of terms approaches infinity.
The sequence {1, 2, 3, 4} does not converge to any real number as the number of terms approaches infinity.
Key Points:
A sequence is a sequence of numbers.
A sequence converges to a single real number as the number of terms approaches infinity.
A sequence converges if the limit of the sequence is a specific real number.
A sequence does not converge if the limit is undefined or infinite