Q: Problems Connecting New iPad Pro With iMac & iTunes

Just bought iPad Pro 9.7. Have 21.7" iMac (2011) with Yosemite (10.10) and iTunes (12.1) Also have private wireless LAN that sees both iMac & iPad Pro devices.

When I tried to USB-connect iPad to iMac, got message that iPad can't be connected because version of the iMac's iTunes app is too old.

{NOTE: I DID FULL iMAC REBOOT IMMEDIATELY AFTER EACH ATTEMPT OF THE FOLLOWING UPDATES/UPGRADES TO iTUNES & iMAC!}

I agreed when iMac asked if I wanted to update iTunes now. iMac indicated a successful update when it finished. BUT, About iTunes still showed old version of iTunes (?), and iMac still wouldn't allow iPad to connect to iMac.

I then decided to attempt the free iMac upgrade from Yosemite to El Capitan. Got indication that this upgrade was successful. But About This Mac doesn't show new version number (?), just as in the iTunes case. And iPad still won't connect to iMac.

These update/upgrade glitches seem very strange to me.

Any suggestions, please, on what I might be doing wrong, or what I might do next to get my iMac OS and iTunes app updated so that I can integrate my new iPad Pro?

THank you.