Kempner series

The Kempner series is a modification of the harmonic series, formed by omitting all terms whose denominator expressed in base 10 contains the digit '9'. That is, it is the sum

where the prime indicates that n takes only values whose decimal expansion has no 9s. The series was first studied by A. J. Kempner in 1914. The series is interesting because of the counter-intuitive result that, unlike the harmonic series, the Kempner series converges. Kempner showed the sum of this series is less than 80. Baillie showed that, rounded to 20 decimals, the actual sum is 22.92067 66192 64150 34816 (sequence A082838 in OEIS)).

单词	Kempner series
释义	Kempner series 英语百科 Kempner series The Kempner series is a modification of the harmonic series, formed by omitting all terms whose denominator expressed in base 10 contains the digit '9'. That is, it is the sum where the prime indicates that n takes only values whose decimal expansion has no 9s. The series was first studied by A. J. Kempner in 1914. The series is interesting because of the counter-intuitive result that, unlike the harmonic series, the Kempner series converges. Kempner showed the sum of this series is less than 80. Baillie showed that, rounded to 20 decimals, the actual sum is 22.92067 66192 64150 34816 (sequence A082838 in OEIS)).
随便看	Hadean aeon的意思 Hadean Eon的意思 hadean eons的意思 Hadean的意思 Hadean time的意思 hadean times的意思 had的意思 Hadeda的意思 hadedah的意思 hadedah ibis的意思 hade的意思 Hadeeth的意思 hadeeths的意思 Hadefield的意思 had egg on my face的意思 had eggs on the spit的意思 Hadego的意思 Hadego film composing machine的意思 Hadejia的意思 Hadejia, R.的意思 Hadeland的意思 hade的意思 Haden hemoglobinometer的意思 Hadeninae的意思 Haden method的意思