# [C (gcc)], <s>112</s> <s>101</s> <s>94</s> 84 bytes

Thanks for the golfing tips from ceilingcat.

<!-- language-all: lang-c -->

    n;f(s){float r;for(n=98;n;r+=pow(n--,-s));printf("%.5f",r+pow(99,-s)*(.5+99./--s));}

[Try it online!][TIO-jp1oveub]

[C (gcc)]: https://gcc.gnu.org/
[TIO-jp1oveub]: https://tio.run/##XcvRCoMgGIbhc69ChMHvTEfbgkS6GBH@CMxCHTuIbn1udTQ8fd7vc3J0rpRgEBLf0C8202hwiRAG3ZtgohjW5Q1BykYmzs0ap5AR2EV1yJoojqj10a6gOqG1uslzuJfZTgE42QilCO3v@soJGOPmhHsNjxqeNfQ1tPpfdlI@Dr0dU5F@/gI "C (gcc) – Try It Online"