Fourth Golden ratio infinite series

I have made the fourth golden ratio infinite series. The first three golden ratio infinite series are already made into blog post and posted earlier.

This blog post is of the fourth infinite series of golden ratio.

Many may say that these are not of golden ratio. I disagree with them. All the infinite series of golden ratio of mine do exhibit golden ratio properties. They may not be half plus root five by two as such; but certainly are maybe 3/2 plus root5 by two or such equations. 

All the infinite series of mine of golden ratio do exhibit golden ratio properties. They may not have a beauty of 1,1,2,3,5,8,13, . . . . . . .  or 1+1/(1+1/(1+1/(1+1/(1+ . . . . . . ; but they are good only.

Have a nice day !!