If x is an ordinary variable, the Maclaurin series for 1/(1 x) is If XÌ is some

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If x is an ordinary variable, the Maclaurin series for 1/(1 ˆ’ x) is

= =1+x² +x³ +x* +...

If XÌ‚ is some operator, show that the series

1 + XÌ‚ + XÌ‚2 + XÌ‚3 + XÌ‚4 +· · ·

is the inverse of the operator 1 ˆ’XÌ‚.

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