+0

# Sum of reciprocals

0
200
1

What is the sum of the sequence: 1/1 + 1/2  +  1/3  + 1/4 +.................+1/1,000? Thank you for help.

Jan 20, 2019

#1
+6099
+2

this is \(H_{1000}\), the 1000th harmonic number.

It is approximately 7.48547

It is exactly

(5336291328229478504559104562404298040965247228038426009710134924845626\
8889497101757506097901985035691409088731550468098378442172117885009464\
3023443265660225021002784256328520814055449412104425101426727702947747\
1270891796396777961045322469242686646888828158207198489710511079687324\
9319155529397017508931564519976085734473014183284011724412280649074307\
7037366831700558002936592350885893602352858528081607595747378366554131\
75508131522517/)\
(7128865274665093053166384155714272920668358861885893040452001991154324\
0875811114994764441519138715869117178170195752565129802640676210092514\
6587100430513107268626814320019660997486274593718834370501543445252373\
9745298963145674982128236956232823794011068809262317708861979540791247\
7545580493264757378299233527517967352480424636380511370343312147817468\
5087845348567802188807537324992199567205693202909939089168748767269795\
0931603520000)

Jan 20, 2019