Sum[expr, {iiminimax}]
evaluates the discrete sum of expr with i ranging from imin to imax.
Sum[expr, {iimax}]
same as Sum[expr, {i, 1, imax}].
Sum[expr, {iiminimaxdi}]
i ranges from imin to imax in steps of di.
Sum[expr, {iiminimax}, {jjminjmax}, ...]
evaluates expr as a multiple sum, with {i, ...}, {j, ...}, ... being in outermost-to-innermost order.

Double sum:

Symbolic sums are evaluated:

Verify algebraic identities:

Infinite sums: