(Business Gmail has an outlook addin that automatically syncs with Outlook at 5.00 / month)

This lady is very knowledgeable and I have gotten many problems with Outlook solved through her advice.

Diane Poremsky
About Diane Poremsky

A Microsoft Outlook Most Valuable Professional (MVP) since 1999, Diane is the author 
of several books, including Outlook 2013 Absolute Beginners Book. She also created 
video training CDs and online training classes for Microsoft Outlook. You can find 
her helping people online in Outlook Forums as well as in the Microsoft Answers and 
TechNet forums.

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Here is an article by her on Slipstick.com: http://www.slipstick.com/outlook/sync-outlook/using-google-calendar-sync-utility-outlook/

Summary:

"At this time, the only way to sync a calendar between Outlook and Google is by using 
a utility"

Diane Poremsky says
January 3, 2015 at 10:18 pm

"I like companionlink and gsyncit - both are reliable and work well."


CompanionLink for Google 

Do you need a solution to sync Outlook and Gmail Calendar and Contacts when Gmail ends 
ActiveSync? CompanionLink keeps Microsoft Outlook and your Google account synchronized. 
Make changes in Outlook and those will upd
ate your Google account. And vice versa. Set the auto-sync feature to automate the entire
process. CompanionLink works with any Google, Gmail, or Google Apps account.

gSyncit
	

gSyncit is an Outlook add-in that allows for two-way synchronization between Google and 
Outlook calendars, contacts, notes, and tasks with your Google account. In addition, gSyn
cit also supports synchronization between Outlook and Toodledo, Pocket Informant Online, 
Evernote, Dropbox, Simplenote and Nozbe. Version 3.6 and higher support Windows 8 and 
Outlook 2013. Supports Outlook 2010 and 2013 64-bit.

This Article shows screenshots for synchronizing Outlook and Gmeil using companionlink and gsyncit: https://www.ablebits.com/office-addins-blog/2013/11/20/sync-google-calendar-with-outlook/