FoldUnfold Table of Contents Evaluating Limits of Recursive Sequences Examples 1 Example 1 Evaluating Limits of Recursive Sequences Examples 1 We will now look at some more examples of evaluating limits of recursive sequences. Be sure to check our the Evaluating Limits of Recursive Sequences page first for more examples. Example 1 Consider the sequence […]

## Evaluating Limits of Recursive Sequences

FoldUnfold Table of Contents Evaluating Limits of Recursive Sequences Example 1 Evaluating Limits of Recursive Sequences Recall that one way to represent a sequence is by a recursive formula. For example, the Fibonacci sequence $\{ 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … \}$ is defined recursively with $f_1 = 1$, $f_2 […]

## Evaluating Limits of Sequences Examples 2

FoldUnfold Table of Contents Evaluating Limits of Sequences Examples 2 Example 1 Evaluating Limits of Sequences Examples 2 We will now look at some more examples of evaluating the limit of a sequence. More examples can be found on the Evaluating Limits of Sequences and Evaluating Limits of Sequences Examples 1 pages. Example 1 Evaluate […]

## Evaluating Limits of Sequences Examples 1

FoldUnfold Table of Contents Evaluating Limits of Sequences Examples 1 Example 1 Example 2 Example 3 Example 4 Evaluating Limits of Sequences Examples 1 We will now look at some more examples of evaluating the limit of a sequence. More examples can be found on the Evaluating Limits of Sequences and Evaluating Limits of Sequences […]

## Evaluating Limits of Sequences

FoldUnfold Table of Contents Evaluating Limits of Sequences Example 1 Example 2 Example 3 Example 4 Evaluating Limits of Sequences We will now look at some examples of evaluating limits of sequences using various approaches and theorems that we have already looked at. More examples can be found on the Evaluating Limits of Sequences Examples […]

## Comparison Theorems for Sequences

FoldUnfold Table of Contents Comparison Theorems for Sequences Comparison Theorems for Sequences We will now look at a few very important comparison theorems for both divergent and convergent sequences. Theorem 1: If $a_n ≤ b_n$ for all $n ≥ N$ and $\lim_{n \to \infty} a_n = \infty$ then $\lim_{n \to \infty} b_n = \infty$. What […]

## The Squeeze Theorem for Convergent Sequences Examples 1

FoldUnfold Table of Contents The Squeeze Theorem for Convergent Sequences Examples 1 Example 1 Example 2 The Squeeze Theorem for Convergent Sequences Examples 1 Recall from The Squeeze Theorem for Convergent Sequences page that if the limits of the sequences $\{ a_n \}$, $\{ b_n \}$, and $\{ c_n \}$ are convergent and $a_n ≤ […]

## The Squeeze Theorem for Convergent Sequences

FoldUnfold Table of Contents The Squeeze Theorem for Convergent Sequences Example 1 The Squeeze Theorem for Convergent Sequences We will now proceed to specifically look at the limit squeeze theorem (law 7 from the Limit of a Sequence page) and prove it’s validity. Law 7 (Squeeze Theorem for Convergent Sequences): If the limits of the […]

## Limit Constant Multiple/Power Laws for Convergent Sequences

FoldUnfold Table of Contents Limit Constant Multiple/Power Laws for Convergent Sequences Constant Multiple Law for Convergent Sequences Power Law for Convergent Sequences Limit Constant Multiple/Power Laws for Convergent Sequences We will now proceed to specifically look at the limit constant multiple and power laws (law 5 and law 6 from the Limit of a Sequence […]

## Limit Product/Quotient Laws for Convergent Sequences

FoldUnfold Table of Contents Limit Product/Quotient Laws for Convergent Sequences Product Law for Convergent Sequences Quotient Law for Convergent Sequences Limit Product/Quotient Laws for Convergent Sequences We will now look at the limit product and quotient laws (law 3 and law 4 from the Limit of a Sequence page) and prove their validity. Product Law […]

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