Write you or Write to youPlease write or write to you
There are other creative ways to start a mailing even then, according to the information contained. For British English, the "to" is mandatory. I' ll write to you........ But" I'll write you a letter..." Across-the-board use of the Amex ='communicating with (one person) in writing' is shown in the following New Yorker episodes.
It used to be a BrE reference ('frequent from 1790' says the OED), but it is now only used to a limited extent if it is not followed by a second (direct) item, as in I will write you a note as soon as I do so. As for the old-fashioned business letters, the guys we sent you last night, please write to us at your will. But today they would usually be added before you and us.
I' ll write to you[or: your company] that..... I' m just saying that..... I come from the darkness of Great Britain and I am a novelist who likes languages. It is already clear that you are talking to someone. Others have already indicated official English for businesses. Well, let's review some possible context of your letter:
Respond to an information inquiry (your mail or e-mail is an answer). Begin always by gratefully acknowledging the questioner and asking the other one: the second time: the first time you ask the question: "They write to revive a preceding dialogue or to clarify some open questions. You write everything as if the other party's lawyer could interpret it - even if everything is in order.
Write also as if YOUR lawyer had written the materials to create a string of incidents that inseparably documents how one thing goes to another, so that if all your mail were designed, each readership could see the evolution of your mail alone. "I am typing to let you know that....." is official in all types of English, and less verbose than your second example, as "for you" is superfluous anyway.
"I' m gonna write you so you know" is not something I'd use. "I' write to you" means "I' write the you." But the Americans use "I'll write you" in an informal way, while in Great Britain it would always be "I'll write to you". But" I'll write you a letter" is okay in Great Britain.
That' proper official UK English: "I' m gonna write you so you know" or "I' m gonna write you so you know"? From a syntactic point of view, the right phrase is: "I write to let you know..... We would say in Anglo-Saxon (British English): "I write to let you know.....
It is really not necessary to say "write to you to let you know", as this is indicated by the title (Dear......) or the name of the recipient and/or the way the mail is delivered. You can''write' a character in relation to your first proposal, so this is wrong. However, I believe that in US (American English) it cannot be wrong to say: "I write to you", in which case the second could also be right in the US.