I am writing a letter.

我正在写信。

I am writing to ask if Class 3 can have a party.

我写信询问三班是否可以举办派对。

I am writing to express my outrage that animals were performing at the circus in West Park.

我写信是为了表达我对动物在西公园马戏团表演的愤怒。

I am writing to inform you that the oil wells in Back Bay are still polluting our rivers and killing the fish.

我写信是为了通知您，后湾的油井仍在污染我们的河流并杀死鱼类。

I am writing a new piece of code.

我正在编写一个新的代码。

At this very moment, I am writing a letter.

此时此刻，我正在写一封信。

I am writing a literature review for my thesis.

我正在为我的毕业论文写一篇文献综述。

I am writing this letter on behalf of my friend.

我代表我的朋友写这封信。

This article is relevant to the paper I am writing.

这篇文章与我正在写的论文相关联。

To whom it may concern, I am writing this letter to recommend Mr. Li.

敬启者，我写这封信是为了推荐李先生。