Question: how to express tanh(x) and tanh(x+1)?

series(1/(1-x), x=0);
can be express as sum(x^y,y=0..infinity)
 
series(tanh(x), x=0);
how to express tanh(x) and tanh(x+1)?
 
is there any function and procedure to generate x^y these kind of result?
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