Comments by "zenith parsec" (@zenithparsec) on "700 years of secrets of the Sum of Sums (paradoxical harmonic series)" video.

"Can you write the numbers 2 and 3 as sums of distinct positive integers?" It really depends on what you mean by 'write'... For 3, [edit] 1/1+ 1/2+ 1/3+ 1/4+ 1/5+ 1/6+ 1/7+ 1/8+ 1/9+ 1/10+ 1/15+ 1/230+ 1/57960 The sum of the reciprocal of all powers of 2 of positive integers sums to 2.... 1/1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + 1/512 + 1/1024 + 1/2048 + 1/4096 + 1/8192 + 1/16384 + 1/32768 + 1/65536 + 1/131072 + 1/262144 + 1/524288 + 1/1048576 + 1/2097152 + 1/4194304 + 1/8388608 + 1/16777216 + 1/33554432 + 1/67108864 + 1/134217728 + 1/268435456 + 1/536870912 + 1/1073741824 + 1/2147483648 + 1/4294967296 + 1/8589934592 + 1/17179869184 + 1/34359738368 + 1/68719476736 + 1/137438953472 + 1/274877906944 + 1/549755813888 + 1/1099511627776 + 1/2199023255552 + 1/4398046511104 + 1/8796093022208 + 1/17592186044416 + 1/35184372088832 + 1/70368744177664 + 1/140737488355328 + 1/281474976710656 + 1/562949953421312 + 1/1125899906842624 + 1/2251799813685248 + 1/4503599627370496 + 1/9007199254740992 + 1/18014398509481984 + 1/36028797018963968 + 1/72057594037927936 + 1/144115188075855872 + 1/288230376151711744 + 1/576460752303423488 + 1/1152921504606846976 + 1/2305843009213693952 + 1/4611686018427387904 + 1/9223372036854775808 + 1/18446744073709551616 + 1/36893488147419103232 + 1/73786976294838206464 + 1/147573952589676412928 + 1/295147905179352825856 + 1/590295810358705651712 + 1/1180591620717411303424 + 1/2361183241434822606848 + 1/4722366482869645213696 + 1/9444732965739290427392 + 1/18889465931478580854784 + 1/37778931862957161709568 + 1/75557863725914323419136 + 1/151115727451828646838272 + 1/302231454903657293676544 + 1/604462909807314587353088 + 1/1208925819614629174706176 + 1/2417851639229258349412352 + 1/4835703278458516698824704 + 1/9671406556917033397649408 + 1/19342813113834066795298816 + 1/38685626227668133590597632 + 1/77371252455336267181195264 + 1/154742504910672534362390528 + 1/309485009821345068724781056 + 1/618970019642690137449562112 + um... I'm going to run out of space, aren't I? now @ 31:52 ... So it looks like I wasn't cheating. and trivial way to represent so here's 4: 1/1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10 + 1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19 + 1/20 + 1/21 + 1/22 + 1/23 + 1/24 + 1/25 + 1/26 + 1/27 + 1/28 + 1/29 + 1/30 + 1/200 + 1/77706 + 1/16532869712 + 1/3230579689970657935732 + 1/36802906522516375115639735990520502954652700 + 1/1!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001 (Replace each ! in that with 1000 zeros, and you get an answer which is accurate to 112120 digits. (Today is 11/21/20, which is why i used that number.) the 'bc' code to get that answer: ms=112120; scale=ms; s=0; for(i = 1; s < 4-(1/10^(scale )); ) { r=1/i; i=i+1; if(s+r < 4) { s=s+r; print "1/",i-1 ," + "; if(s < 4 && s > 4- (1/i) ) { scale=0; i = 1/(4-s); scale=ms; }; }; }; print "\n";
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