What is the largest triangle number that is less than 1000?
Do you mean the largest "triangular number" ?
Triangular numbers are
1 , 3, 6, 10, 15, 21 , ....., n(n+1)/2
so n(n+1)/2 ≤ 1000
n^2 + n ≤ 2000
n^2 + n - 2000 ≤ 0
let's solve the equation
n = (-1 ± √8001)/2 = appr 44.2 or a silly negative
if n = 44 , term(44) = 44(45)/2 = 990
if n = 45 , term (45) = 45(46)/2 = 1035 too big
the largest triangular number < 1000 is 990
To find the largest triangle number that is less than 1000, we first need to understand what a triangle number is.
A triangle number is the sum of the positive integers up to a certain number. For example, the first triangle number is 1 (1 = 1), the second triangle number is 3 (1 + 2 = 3), the third triangle number is 6 (1 + 2 + 3 = 6), and so on.
To find the largest triangle number that is less than 1000, we can start by calculating the triangle numbers and checking if each one is less than 1000.
Here's how we can do it:
1. Set a variable to keep track of the triangle numbers.
2. Start with the first positive integer "n" and set the triangle number to 0.
3. Increment the triangle number by adding "n" to it.
4. Check if the current triangle number is less than 1000.
5. If it is, keep increasing "n" and updating the triangle number. If not, stop and output the previous triangle number.
Let's apply this method step by step:
1. Start with n = 1 and triangle_number = 0.
2. Add n to triangle_number (0 + 1 = 1).
3. Check if the triangle_number (1) is less than 1000. It is, so continue.
4. Increment n by 1 (n = 2) and add n to triangle_number (1 + 2 = 3).
5. Check if the new triangle_number (3) is less than 1000. It is, so continue.
6. Increment n by 1 (n = 3) and add n to triangle_number (3 + 3 = 6).
7. Check if the new triangle_number (6) is less than 1000. It is, so continue.
8. Increment n by 1 (n = 4) and add n to triangle_number (6 + 4 = 10).
9. Check if the new triangle_number (10) is less than 1000. It is not, so the previous triangle_number (6) is the largest triangle number less than 1000.
Therefore, the largest triangle number that is less than 1000 is 6.