Calculus Examples

\infty \sum n = 1 2^{n}

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

Step 1

The series is divergent if the limit of the sequence as

n

$n$ approaches

\infty

$\infty$ does not exist or is not equal to

0

$0$ .

lim n \to \infty 2^{n}

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

Step 2

Since the exponent

n

$n$ approaches

\infty

$\infty$ , the quantity

2^{n}

$2^{n}$ approaches

\infty

$\infty$ .

\infty

$\infty$

Step 3

The limit exists and does not equal

0

$0$ , so the series is divergent.

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