The first time I saw a Mexican Blue Palm (Brahea armata) in flower (inflorescences) I was blown away by how far out and down from the head of the "tree" the flowers hung. As you can see from the image above some of them were hanging down a good 15 feet! A good site for more info on this palm is rarepalmseeds.com It is also a good source of palm seeds of many kinds.
This particular tree in the "paseo del parque" of Malaga, Spain stands about 80 feet tall. In the image above the other palms behind the Mexican Blue Palm are Canary Island Date Palms. Also nearby are some true Date Palms. In the image below you can see what the hanging fruit looks like on a smaller palm.
The leaves are fan like (with pronounced fingers) and on the palms that I have seen range from 2-4 feet wide on 2-4 foot long stems.
The inflorescences gives way to hanging clusters of "fruit" that consists of small balls about the size of walnuts or large grapes. The images below pretty well speak for themselves.