1 Chronicles 16:41
And with them Heman and Jeduthun, and the rest that were chosen, who were expressed by name, to give thanks to the LORD, because his mercy endureth for ever; And with them Heman and Jeduthun, and the rest that were chosen, who were expressed by name, to give thanks to the LORD, because his mercy endureth for ever;
The verse stands in the account of David bringing the ark from Kirjath-jearim to Jerusalem and of the worship that accompanied that occasion. In that setting Heman and Jeduthun and the rest who were chosen, being expressed by name, were appointed to give thanks to the Lord on the ground that His mercy endures forever. The passage to which the verse belongs is parallel to Psalm 105.
Its enduring mercy reaching to a thousand generations is joined with the keeping of God's commandments. Those thousand generations are God's promise to Abraham. That promise belongs not to the Jews by physical descent but to those who are Christ's, and therefore it does not prove that the end of the world is far in the future.