Calculus Examples

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

Step 1

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

$lim_{n \to \infty} \frac{1}{n}$

Step 2

Since its numerator approaches a real number while its denominator is unbounded, the fraction $\frac{1}{n}$ approaches $0$ .

$0$

Step 3

The test is inconclusive because the limit is $0$ .

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