What is the value of the series 1 + 1/2 + 1/3 + ... + 1/n as n approaches infini

What is the value of the series 1 + 1/2 + 1/3 + ... + 1/n as n approaches infinity?

What is the value of the series 1 + 1/2 + 1/3 + ... + 1/n as n approaches infinity?

Step 1: Understand the series 1 + 1/2 + 1/3 + ... + 1/n. This means you are adding fractions where the denominator increases.
Step 2: Recognize that as n gets larger, you keep adding more and more positive numbers (1, 1/2, 1/3, ...).
Step 3: Notice that each term (1/n) gets smaller as n increases, but you are still adding an infinite number of terms.
Step 4: Realize that even though the individual terms get smaller, there are infinitely many of them, so the total keeps growing.
Step 5: Conclude that as n approaches infinity, the sum of the series does not settle at a specific number but keeps increasing without bound.

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