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Evaluating Limits of Sequences Algebraically

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Explanations 1

Finding Limits of Sequences Algebraically In many cases, such as lim⁡n→∞21/n\lim_{n\to\infty} 2^{1/n}limn→∞21/n, we can interpret a sequence limit as a function limit towards i…
By Victor Wang

Problems 2

The sequence defined by an=5−2−na_n = 5-2^{-n}an=5−2−n is convergent. Find the lowest value of kkk such that for any integer i≥ki \ge ki≥k, ∣5−ai∣≤14| 5 - a_i | \le \frac{1}{4}…
The sequence defined by an=3−na_n = 3^{-n}an=3−n is convergent. Find the lowest value of kkk such that for all integers i,j≥ki, j \ge ki,j≥k, ∣ai−aj∣<127| a_i - a_j | < \frac{1…