This gives Golden Ratio phi to 10 places

The above formula gives Golden Ratio to 10 places. It gives 1.6180339887.

You may try this in your calculator and see. Using the Windows 7 calculator will be ideal.

I got agm(7,8,10) as 8.2878898435271

I got agm(1,2,3,4) as 2.3545004777747

You have to be careful with the brackets. 

You may observe that the above equation makes sense considerably. There is a geometric progression equation sort of too.

As the equation is of Golden Ratio, I thought of sharing it.