Marta here from Trello Support.
Depending on the board's settings, if the board admin has determined that only admins can invite other members, you won't see that option in the board's menu.
You can reach out to the admin to change those settings or ask them to add you as an admin as well. Here's an article on how to Change permissions on a board. Also, here are the instructions on Making a user an admin of a board.
I hope that helps! If this doesn't relate to what you're experiencing, please reach out to us here trello.com/contact and we'll be glad to help.
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