Calculus Examples

$lim_{n \to \infty} \sum_{j = 1}^{n} \frac{9 j}{n^{2}}$

Step 1

The formula for the summation of a polynomial with degree $1$ is:

$\sum_{k = 1}^{n} k = \frac{n (n + 1)}{2}$

Step 2

Substitute the values into the formula and make sure to multiply by the front term.

$(9) (\frac{n (n + 1)}{2})$

Step 3

Combine $9$ and $\frac{n (n + 1)}{2}$ .

$\frac{9 n (n + 1)}{2}$