Previous Year NEET Question- Sequence And Series

• 2018:

The sum of the first n terms of the series $1 + \frac{1}{2} + \frac{1}{3} + … + \frac{1}{n}$ is approximately $\ln(n) + \gamma$.

This can be proven by using the following equation:

S = \frac{n}{2}(a + l)

where $S$ is the sum of the series, $n$ is the number of terms, $a$ is the first term, and $l$ is the last term.

In this case, $a = 1$ and $l = \frac{1}{n}$. Substituting these values into the formula, we get:

S = \frac{n}{2}(1 + \frac{1}{n}) = \frac{n}{2}\left(\frac{n + 1}{n}\right) = \frac{n + 1}{2}

Therefore, the sum of the first n terms of the series $1 + \frac{1}{2} + \frac{1}{3} + … + \frac{1}{n}$