Calculus Examples

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

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.

$\frac{\infty (\infty + 1)}{2}$

Step 3

Simplify.

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Step 3.1

A non-zero constant times infinity is infinity.

$\frac{\infty}{2}$

Step 3.2

Infinity divided by anything that is finite and non-zero is infinity.

$\infty$