Calculus Examples

$\sum_{n = 1}^{\infty} 2^{n}$

Step 1

The series is divergent if the limit of the sequence as $n$ approaches $\infty$ does not exist or is not equal to $0$ .

$lim_{n \to \infty} 2^{n}$

Step 2

Since the exponent $n$ approaches $\infty$ , the quantity $2^{n}$ approaches $\infty$ .

$\infty$

Step 3

The limit exists and does not equal $0$ , so the series is divergent.

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