无任的英文：
1.[Formal] immensely; extremely

参考例句：

Feel most grateful
无任感激

Your patronage is cordially invited.
如蒙光顾，无任欢迎。

We would be grateful for prompt payment of your account.
如即付款无任感激.

Please accept this gift in appreciation of all you've done for us
多蒙鼎力协助,无任感谢

Knowing how greatly interested I am in your progress, allow me to congratulate you on this new honour.
闻足下进步之大，无任允欣，如此新荣，殊堪祝贺。

formal是什么意思：
adj. 正式的；礼仪上的；有条理的；正规的；公开的 ；拘谨的

You should recast the report in formal wording as it is a formal occasion.
这是一个很郑重的场合，所以你的报告应改的正式一点。

A formal note is essentially a formal personal letter.
正式照会实质上是正式的个人函件。

They are very formal in their business transactions.
他们的商务议事很有条理。

immensely是什么意思：
adv. 非常；极大地；无限地

The concert was immense.
演唱会非常成功。

The sun is an immense globe.
太阳是一个巨大的球体。

You flatter me immensely!
你太恭维我了！

extremely是什么意思：
adv. 极端地，非常地，很

in an extremity
智尽力竭|陷入绝境

relative extreme
相对极值

It is extremely corrosive.
它是极强的腐蚀剂。