Collins Cobuild

4
You also use ‘I’ll’ to offer to do something.
I’ll give them a ring if you like.
I’ll show you the hotel.
5
You use ‘You must’ if you want to invite someone very persuasively to
do something.
You must come round for a meal some time next week.
You must come and visit me.
6
There are other ways of making offers and giving invitations without
using modals. For example, you can use ‘Let me’ when offering to help
someone.
Let me take you to your room.
Let me drive you to London.
You can make an offer or give an invitation in a more informal way by
using an imperative sentence, when it is clear that you are not giving
an order.
Have a cigar.
Come to my place.
You can add emphasis by putting ‘do’ in front of the verb.

---

Do have a chocolate biscuit.
Do help yourselves.
Do come in, Mr Travis.
You  can  also  give  an  invitation  by  using  ‘Why  don’t  you’  or  ‘How
about’.
Why don’t you come to lunch tomorrow?
How about coming with us to the party?
How about you come and have dinner with me tonight?

---