Equation field guide
Sums and products: repeat an operation over an index
Σ adds a collection of terms. Π multiplies them. The lower and upper labels tell you which terms belong to the collection.
Read a summation
Σ from i = 1 to n of aᵢ means add the entries a₁ through aₙ. The expression after Σ is the term to compute for each i; the bounds determine where to begin and stop.
If the index runs over a set rather than a numerical range, include exactly the members specified by that set. The result is one combined quantity.
Read a product
Π uses the same index and bounds convention, but multiplies the listed terms instead. Π from i = 1 to 3 of i is 1 × 2 × 3 = 6.
A product of many probabilities or growth factors can become very small or very large. Authors sometimes take a logarithm to turn that product into a sum.
Counts and units
A sum over n terms contains n contributions when both endpoints are included and the index advances by one. Check whether the article instead selects a subset.
Terms added in a sum need compatible units. Factors in a product have units that multiply, which can reveal a dimensional mistake.