Fractions, roots and sums

A maths toolkit: amsmath

• For serious maths, load the amsmath package once in the preamble:

\usepackage{amsmath}

• It adds better fractions, alignment, and dozens of symbols. Almost every maths document uses it.

Fractions and roots

• A fraction is \frac{top}{bottom}; a square root is \sqrt{...}:

\[ \frac{a + b}{2} \qquad \sqrt{x^2 + y^2} \]

• They nest happily: \sqrt{\frac{1}{n}} is the square root of one-over-n.

Sums and integrals

• These grow to the right size automatically:

\[ \sum_{i=1}^{n} i \qquad \int_0^1 x^2 \, dx \]

• The _ sets the lower limit and ^ the upper limit — the same keys as powers.

Common mistakes

• \frac, \sqrt or \sum in plain text. Half is \frac{1}{2}. gives ! Missing $ inserted. Put them inside $...$ or \[ ... \].
• Forgetting \usepackage{amsmath}. Commands such as \text{...} then give ! Undefined control sequence.
• \sqrt{3}{x} for a cube root. The root's index goes in square brackets: \sqrt[3]{x}.