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based on an earlier version of the Wolfram Language.
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Ratios

Ratios[list]
gives the successive ratios of elements in list.
Ratios
gives the n^(th) iterated ratios of list.
Ratios
gives the successive ^(th) ratios at level k in a nested list.
  • Ratios divides successive elements by preceding ones, so that Ratios gives .
  • If list has length s, Ratios has length .
  • Ratios or Ratios finds the successive ratios of rows in a 2D array or matrix m. Ratios finds the ratios of columns.
First ratios:
Second ratios:
First ratios:
In[1]:=
Click for copyable input
Out[1]=
 
Second ratios:
In[1]:=
Click for copyable input
Out[1]=
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:
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