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Here's an exercise that is characteristic of "Ragtime" music! Notice that both hands are working with ONLY the notes of a C major chord but in different ways.
The right hand is playing the notes of a C major chord one at a time in this pattern:
G - C - E - G - E - G - E (repeat)
While the left hand is alternating between two different inversions of a C major chord:
C - then E & G together
Down to a lower G - then C & E together (repeat)
Play it slowly at first and gradually build up speed.