Calculus: Mathematical Induction

User Generated

xngtvey

Mathematics

Description

Ten multiple choice questions. Do not have to show work. Questions involve finding Pk+1 and other mathematical induction questions. File is attached.

Unformatted Attachment Preview

Find Pk+1 if 𝑃𝑘 = 2𝑘−1 𝑘! A B C D Find Pk+1 if Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1) 7 + 13 + 19 + …+[6(k - 1) + 1] + (6k + 1) + [6(k + 1) + 1] 8 + 14 + 20 + …+[7(k - 1) + 1] + (7k + 1) 7 + 13 + 19 + …+(6k + 1) 7 + 13 + 19 + ...+[6(k - 1) + 1] + (6k +1) + (6k + 2) What is the first step when writing a proof using mathematical induction? Assume that formula is true for Pk. Find Pk+1. Verify formula is true for P1. Find the sum of the integers. Which of the following shows the correct first step to prove the following by mathematical induction? 3 + 11 + 19 + 27 + … + (8n - 5) = n(4n - 1) 3 + 11 + 19 + 27 + … + (8 • 1 - 5) = 1(4 • 1 - 1) 8 • 1 - 5 = 1(4 • 1 - 1) 3 + 11 + 19 + 27 + … + (8k - 5) = k(4k - 1) 3 + 11 + 19 + 27 + … + (8k - 5) + [8(k + 1) - 5] = (k + 1)[4(k + 1) - 1] Which of the following shows the best next step to prove the following by mathematical induction? A B C D Which of the following shows the best next step to prove the following by mathematical induction? A B C D Which of the following shows the best next step to prove the following by mathematical induction? A B C D Find the second difference for the sequence. 7, 6, 7, 10, 15, 22, …. 1 2 3 5 Find first differences for the sequence in order from a1 to a5. Determine whether or not the series is quadratic or not. -1, -3, -1, 5, 15 2, 2, 6, 10; not quadratic 2, 2, 6, 10; quadratic -2, 2, 6, 10; not quadratic -2, 2, 6, 10; quadratic Find a quadratic model for the sequence. -4, -4, -3, -1, 2 y = 0.5x2 - 0.5x - 4 y = 0.5x2 - 1.5x - 3 y = 4.5x2 - 21.5x+21 y = -4.5x2 + 21.4x - 21
Purchase answer to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

Attached. Hope all of them are correct.

Find Pk+1 if

=

!

A
B
C
D

Find Pk+1 if
Pk = 7 + 13 + 19 + ...+[6(k - 1)+1] + (6k + 1)

7 + 13 + 19 + …+[6(k - 1) + 1] + (6k + 1) + [6(k + 1) + 1]
8 + 14 + 20 + …+[7(k - 1) + 1] + (7k + 1)
7 + 13 + 19 + …+(6k + 1)
7 + 13 + 19 + ...+[6(k - 1) + 1] + (6k +1) + (6k + 2)

What is the fi...


Anonymous
Awesome! Perfect study aid.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags