Please, if possible, circle the answer so that I can understand the steps. Please write clearly if you write by hand so that I can read the numbers. I appreciate your understanding.This question has three parts, and here is the second part, and I will send you the second and third parts separately 4To continue the proof by induction, begin with 4 + 16 + 64 + ... + 4^ =OA. 4-1OB. 4kC. +14k+OD. 4k-1Add this term to both sides of the equation.4 + 16 +64 + ... ++4k4 + 16 +64 + ++4 + 16 +64 +...+ 4 + 4=k+1=44k + 13k+13-4- 4+3Simplify the right side so that it looks similar to the right side of the equation in the original statement.(Do not factor.)The right side of the above equation is Sk+ 1. Is the proof complete?- 4which is assumed to be true, and add the k + 1 term to both sides of the formula. What is this term?O A. No, since it must be shown that S₁ + 1 satisfies the statement.B. No, since it must be shown that S₁ satisfies the statement.C. Yes.D. No, since it has only been shown that Sk + 1 satisfies the statement.

Principle of mathematical induction: If P(n) be a statement and n is natural number. Step 1: Verify…

To continue the proof by induction, begin with 4 + 16 +64 ++4 OA. 4-1 0 в. 4к OC. 4k+1 OD. 4K-1 Add this term to both sides of the equation. 4k+1-4 3 4k+1 3 4+16+64 ++4k = 4+ 16 +64 +...+4K + -4 3 which is assumed to be true, and add the k+ 1 term to both sides of the formula. What is this term? Simplify the right side so that it looks similar to the right side of the equation in the original statement. 4+16+64 +...+4K +4k+ 1 = (Do not factor.) The right side of the above equation is Sk+1. Is the proof complete? OA. No, since it must be shown that Sn+ 1 satisfies the statement. OB. No, since it must be shown that S, satisfies the statement. OC. Yes. OD. No, since it has only been shown that Sk+ 1 satisfies the statement.

To continue the proof by induction, begin with 4 + 16 +64 ++4 OA. 4-1 0 в. 4к OC. 4k+1 OD. 4K-1 Add this term to both sides of the equation. 4k+1-4 3 4k+1 3 4+16+64 ++4k = 4+ 16 +64 +...+4K + -4 3 which is assumed to be true, and add the k+ 1 term to both sides of the formula. What is this term? Simplify the right side so that it looks similar to the right side of the equation in the original statement. 4+16+64 +...+4K +4k+ 1 = (Do not factor.) The right side of the above equation is Sk+1. Is the proof complete? OA. No, since it must be shown that Sn+ 1 satisfies the statement. OB. No, since it must be shown that S, satisfies the statement. OC. Yes. OD. No, since it has only been shown that Sk+ 1 satisfies the statement.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Please, if possible, circle the answer so that I can understand the steps. Please write clearly if you write by hand so that I can read the numbers. I appreciate your understanding.
This question has three parts, and here is the second part, and I will send you the second and third parts separately

4
To continue the proof by induction, begin with 4 + 16 + 64 + ... + 4^ =
OA. 4-1
OB. 4k
C. +1
4k+
OD. 4k-1
Add this term to both sides of the equation.
4 + 16 +64 + ... +
+4k
4 + 16 +64 + +
+
4 + 16 +64 +...+ 4 + 4
=
k+1
=
4
4
k + 1
3
k+1
3
-4
- 4
+
3
Simplify the right side so that it looks similar to the right side of the equation in the original statement.
(Do not factor.)
The right side of the above equation is Sk+ 1. Is the proof complete?
- 4
which is assumed to be true, and add the k + 1 term to both sides of the formula. What is this term?
O A. No, since it must be shown that S₁ + 1 satisfies the statement.
B. No, since it must be shown that S₁ satisfies the statement.
C. Yes.
D. No, since it has only been shown that Sk + 1 satisfies the statement.

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