This is the sequence 1,3,6,10,15 the pattern is addin 1 more than last time but what is the name for this pattern These are called the triangular numbers The sequence is 1 3=1+2 6=1+2+3 10=1+2+3+4 15=1+2+3+4+5 You can also observe this pattern
The numbers 1, 3, 6, 10, 15 are called triangular numbers because they represent the number of objects needed to make triangular arrays as shown below: 16. 10 15 What is the 100th triangular number? Give your rationale.
10. The following triangular arrays of dots led the early Greeks to call the numbers 1, 3, 6, 10, 15, ... triangular num- bers just as 1,4,9,16,.. are called square numbers and can be associated with square arrays of dots. Since 1 = 1, 1+ 2 = 3, 1+ 2+ 3 = 6, 1 + 2 + 3 + 4 = 10, and so on, it is clear that the nth triangular number is given by the formula t(n)=1+2+ …+n="...
Please help and please be as detailed and clear as possible!! Thank you!! ule 3: Greek Mathernaties x D assign9. spring2019.pdf 赝Area of a Circle by Cutting intc | × G area af a circle . Google Searc x × С https://earken edut to s . LexisNexis. Acad. D Apple et duvlid-9415706-dt-content įd-130483512 iCloud Dooogle Dwikipedia r Facebook /coursesns460 15477.201910/ass g a spring20 Q Pau d The weather Cna. Dvelp Dn) Twitter O YouTube a www amazon.com 4. (6 points)...
points PooleLinAlg4 5.3.017 1 The columns of Q were obtained by applying the Gram-Schmidt Process to the columns of A. Find the upper triangular matrix R such that A QR 2 10 6 5 A=110 10-3 , Q = Need Help?Read It Talk to a Tutor + -1 points PooleLinAJg4 5.3.018. The columns of Q were obtained by applying the Gram-Schmidt Process to the columns of A. Find the upper triangular matrix R such that A = QR. (Enter sqrt(n)...
4. The Pell sequence P, P... is defined by P-1, P-2, and P-P-2+2P- for n 3. Define T E C(R") by T(z, y)-(y,x + 2y). (a) Prove that T"(0,1) (PP+) for every integer n1 (b) Find the eigenvalues of T. (c) Find a basis of R2 consisting of eigenvectors of T. (d) Use the solution to part (c) to compute T (0,1. Hint: Write (0,1) as a linear combination of eigenvectors.] (e) Use your answers to parts (a) and (d)...
6. Consider the sum of the first 10 numbers: 1+2+3+4+5+6+7+8+9+10. Can you change some of the plus signs to minus signs so that the resulting sum is 0? For example: 1+2-3-4-5-6+7-8+9+10=3. This is close, but not 0. Provide a solution or show that there isn't one.
Please help me for all problems 1, 2, 3, 4, 5 1. (Three points.) Convert this system to upper triangular form and solve by back-substitution. 4x+7y + 5z 13 -2y + 2z-6 2. (Three points.) Convert this system to upper triangular form and solve by back-substitution. 4x-5y +z=-13 2x -y-3z5 3. (Four points.) Find the value a that will make the matrix of coefficients for this system singular and the value b that will give the system infinitely many solutions...
i need help with number 3&4 and the answer is in red i just need to know how to work the problem (a) y (b) y=-x3 + 6x2-9x + 3 2. The sum of two nonnegative numbers is 36 (a) Find the two numbers if the differ ence of their square roots is to be as large as possible. 0 and 36 (b) Find the two numbers if the sum of their square roots is to be as large as...
Emergency please!!!! Last two numbers digit: 11 1) (35 pts) In this problem the last two digits of your student number will be important. Let n, be a number equal to the last digit of your student number, na be a number equal to the last two digits of your student number. That is, if the last two digits of your student number is 83 then, n = 3, n2 = 83. Consider the predator-prey equations: dx =ax - bxy...
can i get some help with this program CMPS 12B Introduction to Data Structures Programming Assignment 2 In this project, you will write a Java program that uses recursion to find all solutions to the n-Queens problem, for 1 Sns 15. (Students who took CMPS 12A from me worked on an iterative, non-recursive approach to this same problem. You can see it at https://classes.soe.ucsc.edu/cmps012a/Spring l8/pa5.pdf.) Begin by reading the Wikipcdia article on the Eight Queens puzzle at: http://en.wikipedia.org/wiki/Eight queens_puzzle In...