FoldList

FoldList[f, x, {a, b, ...}] gives {x, f[x, a], f[f[x, a], b], ...}.

FoldList[f, {a, b, c, ...}] gives {a, f[a, b], f[f[a, b], c], ...}.

Examples

Cumulative sums:

FoldList[Plus, 0, {1, 2, 3, 4}]
(* {0, 1, 3, 6, 10} *)

Build nested expressions:

FoldList[f, x, {a, b, c}]
(* {x, f[x, a], f[f[x, a], b], f[f[f[x, a], b], c]} *)

Please visit the official Wolfram Language Reference for more details.