Math ( Number Theory )
posted by Lucy .
How many numbers
from 1 to 1000
inclusive can be
expressed as the sum
of k >= 2 consecutive
positive integers for
some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...

Hmmm.
For k=2, we want all n<=1000 such that n=m+m+1 = 2m+1
That is, all odd numbers 3<=n<=999
There are 996/2+1 = 499 of those
For k=3, we want n=3m+3
so, that's all multiples of 3 with 6<=n<=999
There are 993/3+1 = 332 of those
For k=4, we want 4m+6
so, that's all multiples of 4 with 10<=n<=998
There are 988/4+1 = 248 of those
There's a pattern here, so you should be able to come up with some
∑
k=2
expression, or just bruteforce your way through.
Maybe not a lot of help, but it does show that there are more than 997 of them. 
The ans Steve gave is absolutely wrong...the ans is less than 823 and greater than 665...steve u have counted the same numbers more than one time...for example u have counted 15 twice....

When I calculated out I got 990 as the correct answer.
Respond to this Question
Similar Questions

math, algebra
2a+2ab+2b I need a lot of help in this one. it says find two consecutive positive integers such that the sum of their square is 85. how would i do this one i have no clue i know what are positive integers.but i don't know how to figure … 
Math
Most natural numbers can be expressed as a sum of two or ore consecutive positive intergers. Find all natural numbers between 1,000 and 10,000 which cannot be expressed as a sum of tow or more consecutive positive intergers. 
math
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33 
math
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33 how do you solve … 
Algebra
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive … 
Maths
The number 1000 can be written in several ways as a sum of one or more consecutive positive integers, for instance, 1000=1000 (one summand) or 1000=198+199+200+201+202 (five summands). Find the largest possible number of summands in … 
math
The sum of squares formula is given by 1^2+2^2+3^2+…+n^2=n(n+1)(2n+1)/6. The sum of odd squares can be expressed as 1^2+3^2+5^2+…+(2n−1)^2=An^3+Bn^2+Cn+D. The value of A can be expressed as ab, where a and b are positive … 
Math (algebra)
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number? 
Math
1. Set I contains six consecutive integers. Set J contains all integers that result from adding 3 to each of the integers in set I and also contains all integers that result from subtracting 3 from each of the integers in set I. How … 
Math
The number of ways in which 63 can be expressed as a sum of two or more consecutive positive integers.