Suppose you're in a situation where you have a formal/business relationship with someone, but the relationship has become more familiar over time. The other person continues to call you usted. How can you politely ask them to begin referring to you in the tú form? Is it ever inappropriate (by situation or geography) to ask to be referred to in the tú form instead of usted?
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In Spain we would say either of these:
Or, in a more indirect way:
Any of them in a cheerful manner and usually accompanied by the perceptive "por favor" if needed.
You can say in a cheerful tone:
It might be helpful to precede the sentence with an encouragement word, like this:
Please note that this applies particularly to Latin-American Spanish speakers. Some parts of Spain (and Argentina!) could be more conservative regarding the use of 'tú' and instead use the older 'vos'.
I understand that both of you are using “usted” with each other. In that case, in my opinion, it's inappropriate to address them using “tú”, even if it's to ask them to use “tú” towards you.
You should just politely propose that you start using “tú” between each other. Some options:
But if the situation is asymmetric, and you already treat them with familiarity, then use some of the proposals in the other answers.