It is correct: 1) I do hope you will consider me for the job. 2) I hope you will consider me for the job.
If they are both correct is there any difference?
It is correct: 1) I do hope you will consider me for the job. 2) I hope you will consider me for the job.
If they are both correct is there any difference?
They are both correct. We place do before the verb to give emphasis as Fumble Fingers said. We can also do that in the Past Simple with did. For example:
I knew the truth. I did know the truth.
From my experience, your use of "do" more often happens in BrE than AmE, and it is used for emphasis.
Please do let us know how you get on. (BrE)
please be sure to let us know how you are doing / how things are going. (AmE)I do so want you to attend my wedding.
I really want you to attend my wedding.