How to send invitation directly to somebody's calendar.

That is possible when using Calendar integration with one of the supported email/calendar providers. Please check this link for the requirements and setup information: https://support.zoom.us/hc/en-us/articles/360000488243-Setting-up-calendar-and-contacts-integration 

For example: if you're using Google email and calendar, setting this up along with the add-on would allow you to see your Zoom meetings in your Google calendar, and send email invites directly from there. More information on using the add-on can be found here:

https://support.zoom.us/hc/en-us/articles/360020187492-Zoom-for-GSuite-add-on 

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Within Zoom natively this cannot be done however you can use the APIs to trigger a calendar invitation with the relevant Zoom invitation that would be sent directly to an invitee's calendar. One Zoom app that lets you do this is Salepager that sends direct calendar invitations for Zoom meetings and webinars.