This is documentation for Mathematica 7, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Ratios

Ratios[list]
gives the successive ratios of elements in list.
Ratios[list, n]
gives the n^(th) iterated ratios of list.
Ratios[list, {n1, n2, ...}]
gives the successive nk^(th) ratios at level k in a nested list.
  • Ratios divides successive elements by preceding ones, so that Ratios[{x1, x2}] gives {x2/x1}.
  • If list has length s, Ratios[list, n] has length s-n.
  • Ratios[m, {1, 0}] or Ratios[m, 1] finds the successive ratios of rows in a 2D array or matrix m. Ratios[m, {0, 1}] finds the ratios of columns.
  • Ratios[list, {n1, n2}] is equivalent to Ratios[Ratios[list, n1], {0, n2}].
First ratios:
Second ratios:
Ratios of rows, within each column:
Ratios of columns, within each row:
First ratios are constant for a geometric sequence:
FoldList with Times acts as an inverse of Ratios:
New in 7