to inform something to you 说法不对,而且句子有点罗嗦,
这样简洁化就可了：
I am writing to tell you ...
I am writing to inform you ...
The reason for writing this is to inform you that ...
然后接下去写出你的原因.比如
I am writing to inform you of my decision to apply for admission to another university.
The reason for writing this is to inform you that I have decided to apply to another university.