Usage Note
Infiniment is frequently used as a polite intensifier, especially in formal registers: je vous remercie infiniment (thank you so much / thank you infinitely). It is stronger and more literary than beaucoup and lends a courteous, slightly old-fashioned tone to expressions of gratitude.
Examples
"Je vous remercie infiniment de votre aide."
Natural Translation
I thank you enormously for your help.

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