Output the simplified Goodstein sequence

Python 2, 77 74 bytes

-3 bytes thanks to Lynn

n=input();b=1
while n:print"+".join(n/b*[`b`]+[`n%b`][:n%b]);n+=n/b-1;b+=1

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Easily runs up to n = 100 (though the output is too long for tio fully show).

Pyth, 29 bytes

WQ=hZj\++*]Z/QZ<]J%QZJ=+Qt/QZ

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Mathematica, 123 bytes

(s=1~Table~#;i=1;While[s!={},Print@StringRiffle[ToString/@s,"+"];s=s/.i->i+1;s=Join[Most@s,{Last@s}-1]~DeleteCases~0;i++])&

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