Ok, here goes.
You should practice all inversions TOGETHER, this will help your technique and finger precision.
So lets use C maj as an example.
So you start with C (I generally do 4 octaves so lets do this), you go, C E G C (1st inversion) E G C E (2nd inversion) G C E G (3rd inversion), and back to root. So now youve done 1 octave. So keep goin like this for two more octaves and then...
4th Octave
Go C E G C, E G C E, G C E G and then back to the root with a bit of a turn for you to be able to go back down again with no problem so you use the root C E G E C (see the turn, instead of going directrly to C you repeat the E so the last C you play is converted to the FIRST C of the arpeggio that you will play going down this time).
Now for the arps going down.
You continue going down C G E C (root), G E C G (2nd), E C G E (3rd) and back to root. You continue this pattern until you get to the octave where you started. Here you will also do a turn when you get to the final root, go
C G E G C. (The turn being between G and E)
Do this with both hands using a 1 2 3 5 (root), 1 2 4 5 (second), 1 2 4 5 (third), 1 2 3 5 (root) fingering for the right and a 5 3 2 1 (root), 5 4 2 1 (second), 5 3 2 1 (third), 5 3 2 1 (root) for the left (this is for going up, just invert when you go down).
Remember this finguering is for the C maj as arps in other scales may vary.
Now this method is the method used in Russia (my teacher is russian and went to a big conservatory in Moscow, dont remember the name of the conservatory. This is in a book she gave me and she told me this is the best way to practice arpeggios and truly the results are marvelous).
Hope it helps
