#JavaScript, 19 18 bytes
1 byte saved thanks to @RichHitchcock
f=a=>a&&1/a+f(--a) This is 1-indexed.
f=a=>a&&1/a+f(--a) for(i=0;++i<10;)console.log(f(i)) user41805
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#JavaScript, 19 18 bytes
1 byte saved thanks to @RichHitchcock
f=a=>a&&1/a+f(--a) This is 1-indexed.
f=a=>a&&1/a+f(--a) for(i=0;++i<10;)console.log(f(i))