MathDB

1

Part of 2012 BMT Spring

Problems(2)

Sprind Round (2012) #1

Source:

12/3/2012
Let {an}n=1∞ \{a_n\}_{n=1}^\infty be an arithmetic progression with a1>0 a_1 > 0 and 5⋅a13=6⋅a19 5\cdot a_{13} = 6\cdot a_{19} . What is the smallest integer n n such that an<0 a_n<0 ?
arithmetic sequence
2012 BMT Team 1

Source:

1/5/2022
Let SS be the set of all rational numbers x∈[0,1]x \in [0, 1] with repeating base 66 expansion x=0.a1a2...ak‾=0.a1a2...aka1a2...ak...x = 0.\overline{a_1a_2 ... a_k} = 0.a_1a_2...a_ka_1a_2...a_k... for some finite sequence {ai}i=1k\{a_i\}^{k}_{i=1} of distinct nonnegative integers less than 66. What is the sum of all numbers that can be written in this form? (Put your answer in base 1010.)
number theory