ImageMagick is truly a magical tool for images. It makes it super-easy to create an animated GIF file from a series of image files.
To create an animated GIF from 3 input images with a delay of 2 seconds between each frame and loop infinitely:
$ convert -delay 200 -loop 0 1.png 2.png 3.png out.gif
Tried with: ImageMagick 126.96.36.199 and Kubuntu 16.04