I hate to be "that guy" but Frodo never destroys the ring, Frodo failed in his quest and at the end succumbed to the power of the ring. It was only by chance that Gollum fell from the ledge when he was dancing in joy over having regained his "precious".
The light sprang up again, and there on the brink of the chasm, at the very
Crack of Doom, stood
Frodo, black against the glare, tense, erect, but still as if he had been turned to stone.
'Master!' cried
Sam.
Then Frodo stirred and spoke with a clear voice, indeed with a voice clearer and more powerful than Sam had ever heard him use, and it rose above the throb and turmoil of
Mount Doom, ringing in the roof and
walls.
'I have come,' he said. 'But I do not choose now to do what I came to do. I will not do this deed. The
Ring is mine!' And suddenly, as he set it on his finger, he vanished from Sam's sight. Sam gasped, but he had no chance to cry out, for at that moment many things happened.
Something
struck Sam violently in the back,... and he was flung aside, striking his head against the stony floor.... [All] went black.
And far away, as Frodo put on the Ring and claimed it for his own, even in
Sammath Naur the very heart of his
realm, the
Power in
Barad-dûr was
shaken.... The
Dark Lord was suddenly aware of him....