I animated these and related 'proofs' some time ago

    1/3 = 1/4 + 1/16 + 1/64 + ...

https://evanberkowitz.com/images/2014-03-15-quarters/Triangl...

    1/7 = 1/8 + 1/64 + 1/512 + ...

    1/8 = 1/9 + 1/81 + 1/729 + ...