Extension: Triangular Numbers
Read this topicExplanations 3
- The triangular numbers are a useful sequence of numbers, named after the fact that they can be arranged in a triangle as follows: One way to find the nthn^{th}nth triangular num…
By Cameron Montag
- Triangular Numbers We have learned about natural numbers and and perfect numbers. We've also learned about square numbers, like 444 and 161616. You may also be familiar with hex…
By Anusha Rahman
- (Video) Triangular Numbers Explained by Minity Maths In this video by Minity Maths, you will get an explanation for what triangular numbers are and the patterns associated with …
By Anusha Rahman
Problems 9
- You are at a meeting that has 131313 people. Everybody at the meeting shakes hands with everybody else, and nobody shakes hands with the same person more than once. How many han…
- Convert the following recursive formula for g(n)g(n)g(n) to an explicit formula. g(0)=0g(0) = 0g(0)=0 g(1)=1g(1) = 1g(1)=1 g(n)=n+g(n−1)g(n) = n + g(n-1)g(n)=n+g(n−1)
- Find the smallest three-digit triangular number.
- Say we choose a positive integer nnn at random. What is the probability that the nthn^{th}nth triangular number is even?
- Is the 101st101^{st}101st triangular number even or odd?
- Say that an integer n≥2n \ge 2n≥2 is delicious if there exist nnn positive integers adding up to 201420142014 that have distinct remainders when divided by nnn. What is the smal…
- There are NNN students in a class. Each possible nonempty group of students selected a positive integer. All of these integers are distinct and add up to 201420142014. Compute t…
- What is the sum of the reciprocals of the all the nonzero triangular numbers?
- What is the value of Tm+n−Tm−Tn?T_{m+n}-T_m-T_n?Tm+n−Tm−Tn?