query: The series of reciprocals of the integers that do not contain 9 in their decimal representation
positive_passages.docid: 18064
positive_passages.text: Sum of reciprocals of numbers with certain terms omitted
negative_passages.docid: 9343
negative_passages.text: Why does $\frac{1 }{ 99989999}$ generate the Fibonacci sequence?
negative_passages.docid: 20713
negative_passages.text: The sum of an uncountable number of positive numbers
negative_passages.docid: 151375
negative_passages.text: There are $3$ Zero-Sum Numbers!
negative_passages.docid: 151384
negative_passages.text: Summation of series involving binomial coefficients and polynomial of degree at most n-1
negative_passages.docid: 143620
negative_passages.text: How many $n$-digit decimal sequences (using the digits $0 = 9$) are there in which the digits $1$, $2$ and $3$ all appear?
negative_passages.docid: 90074
negative_passages.text: Show that the sequence $1,2,3,4,5,6,7,8,9,1,0,1,1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,2,0,2,1,\cdots$ isn't periodic
negative_passages.docid: 136885
negative_passages.text: Series of natural numbers which has all same digits
negative_passages.docid: 103581
negative_passages.text: Which positive integers can NOT be written as a sum of consecutive positive integers
negative_passages.docid: 148906
negative_passages.text: Finding integers $m,n$ such that $(m-n)^2=4mn/(m+n-1)$
negative_passages.docid: 86194
negative_passages.text: Infinite series with the binomial coefficient
negative_passages.docid: 60965
negative_passages.text: Representing a nonnegative integer as the ordered sum of odd numbers
negative_passages.docid: 135955
negative_passages.text: Prove: The positive integers cannot be partitioned into arithmetic sequences (using Complex Analysis)
negative_passages.docid: 96846
negative_passages.text: Decimal representation begins with $N$
negative_passages.docid: 94871
negative_passages.text: Sum of an unorthodox infinite series
negative_passages.docid: 138267
negative_passages.text: What is the sum of Fibonacci reciprocals?
negative_passages.docid: 119891
negative_passages.text: Divisibility and the Fibonacci sequence