Consider the following patterns:
1=11=1
1+3=41+3=4
1+3+5=91+3+5=9
1+3+5+7=161+3+5+7=16
1+3+5+7...+2n−1=?1+3+5+7...+2n−1=?
Do you see the pattern?
Can you write it in summation notation?
2) Can you provie it as a theorem using induction?
Consider the following patterns: 1=11=1 1+3=41+3=4 1+3+5=91+3+5=9 1+3+5+7=161+3+5+7=16 1+3+5+7...+2n−1=?1+3+5+7...+2n−1=? Do you see the pattern? Can you...
please hell with 13, 14, 15, 16, 17
13. Use the binomial theorem to expand: (w-11) 14. Use mathematical induction to prove the following: 3+ 7 + 11 + 15 + ... + (4n-1) = n(2n+1) 15. Write an expression for the n" term of the sequence 2! 3! 4! 5! 6! 7! 4'5'6'7'8'9' 16. The sixth term of an arithmetic sequence is 20.6, and the ninth term is 30.2. a. Find the nth term b. Find the 20 term...
1. Evaluate the following determinant. -3 -8 11 7 -2 4 5 6 91
Accumulation Pattern Problem 2 Consider the code below. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 labs = ['lab1', 'lab2', 'lab3', 'lab4', 'lab5', 'lab6', 'lab7', 'lab8', 'lab9'] graded = '' for lab in labs: lab_num = int(lab[3]) if lab_num < 4: graded = graded + lab + ' is simple\n' elif lab_num < 7: graded = graded + lab + ' is ok\n' else: graded = graded + lab + ' is complex\n' ...
what is the pKa?
H -10 -6 -4 -2 0 3-5 5-7 9-11 12. 15-16 18 25 30 36-40 41 44 50
Consider the matrix: 15 9 13 2 6 10 14 3 7 11 15 4 8 12 16 a- Find the eigenvectors of this matrix and their corresponding eigenvalues. b-Indicate if there are any degeneracy, and if so, change only one element of this matrix to remove this degeneracy (of course you need to recompute the eigenvalues to show that the degeneracy was lifted). Write a Mathematica program to calculate the roots of the following function f(x) = 0.5*e*-5*x+2 using...
Essay questions
1. in exercise 6.3 step 5, what can you say about the assumption
of constant variance?
2. in exercise 6.3 step 7, what can you say about the assumption
of constant variance?
3. in exercise 6.3 step 8, what can you say about the assumption
of normality
Exercise 6.3 Let us consider the salary (y), the years of experience(K1) and the years of schooling (X2) for 50 employees of the Georgia Pacific Company in Crossett, Arkansas. Our goal...
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 patternThese 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 x _________ x xx __________ x xx xxx __________ x xx xxx xxxx to see why they're called triangular numbers. I think the Pythagoreans (around 700 B.C.E.) were the ones who gave them this name. I do know the...
Below are three statements that can be proven by induction. You do not need to prove these statements! For each one: clearly state the predicate involved; state what you would need to prove in the base case; clearly state the induction hypothesis in terms of the language of the proposition (i.e., without using notation to represent the predicate); and then clearly state the inductive step in terms of the language of the proposition. 1. For all positive integers n, 3...
can you do 11 and 12
please.
E C 7. If AE-3, AB 5, and AD 4, find AC. 8. If AD-5, AB = 8, and AC = 7, find AE. 9. If BD = 3, EC = 4, and AC-9, find AD. 10. If AD = EC, DB = 4, and AE = 9, find AD. 11. If DE5, BC 7, and AD4, find AB. 12. If ED = 7, BC = 10, and AE = 2 + EC,...
11: I can identify the predicate being used in a proof by mathematical induction and use it to set up a framework of assumptions and conclusions for an induction proof. Below are three statements that can be proven by induction. You do not need to prove these statements! For each one clearly state the predicate involved; state what you would need to prove in the base case; clearly state the induction hypothesis in terms of the language of the proposition...