“show you.” The Hebrew is more idiomatic: “make you know something.”
“Come up after me, for Yahweh has given them into the hand of Israel.” Jonathan certainly had revelation from Yahwah as to what to do by this time, and speaks with the calm assurance of one who knows the will of God. We see the same confident talk when David challenged Goliath (1 Sam. 17:45-47). But God’s revelation does not guarantee victory, it must be accompanied by trust in God and willingness to do the hard work at hand. Jonathan and his armorbearer still had to fight to win the battle.