Did David kill Goliath with his sling or with a sword?

Verse 50 sums up the fight; verse 51 then tells how it ended. Hebrew narrative often states the result first and then gives the details, and Keil and Delitzsch read verse 50 in just this way, as the writer’s remark on the outcome. Its point is the contrast the whole chapter has built up: Goliath came “with a sword, and with a spear, and with a shield”, and David “in the name of the Lord of hosts” (1 Samuel 17:45). David won that contest without a sword of his own.

Verse 51 shows how the victory was completed. The stone felled the giant, who “fell upon his face to the earth” (17:49), but he was not necessarily dead. So David ran, stood over him and finished him with his own sword. The Hebrew marks the difference. Verse 50 uses vaymitehu, the ordinary ‘and he killed him’ (Hiphil of muth, Strong’s H4191). Verse 51 uses vaymotetehu, a stronger form (the Polel) which the Brown–Driver–Briggs lexicon glosses ‘kill, put to death, despatch’. Among other places, it is used for finishing off wounded men: Abimelech asking his armour-bearer to kill him (Judges 9:54), Jonathan’s armour-bearer dispatching the Philistines his master had struck down (1 Samuel 14:13), and the Amalekite’s claim about Saul, “I stood upon him, and slew him” (2 Samuel 1:10). The stone brought Goliath down and the sword ended his life, so both verses are true of the one fight.