Q2. Induction. For each integer n > 1, define the sum S(n) as follows: 1 1 1 1 1 S(n) = (2i — 1)(2і + 1) 3.5 5- 7 (2n – 1)(2n + 1)* n=1 1 2 1 1 For example S(1) =E and S(2) = %3D %3D (2i – 1)(2i +1) 1.3 (2i – 1)(2i + 1) 1-3 3-5 n=1 i=1 - i. Compute each of the following values of S(n) and write your final answer as a fraction in lowest terms. S(3) = S(4) = S(5) = - ii. Do you see a general pattern for the simplified value of S(n)? Write your guess to complete the proposition P(n) below. For each integer n > 1, let P(n) be the proposition defined as follows: 1 P(n): S(n) = E (2i – 1)(2i + 1) i=1 – iii. Prove that the proposition P(n) is true for all n 21 using a Proof by induction.

Q2. Induction. For each integer n > 1, define the sum S(n) as follows: 1 1 1 1 1 S(n) = (2i — 1)(2і + 1) 3.5 5- 7 (2n – 1)(2n + 1)* n=1 1 2 1 1 For example S(1) =E and S(2) = %3D %3D (2i – 1)(2i +1) 1.3 (2i – 1)(2i + 1) 1-3 3-5 n=1 i=1 - i. Compute each of the following values of S(n) and write your final answer as a fraction in lowest terms. S(3) = S(4) = S(5) = - ii. Do you see a general pattern for the simplified value of S(n)? Write your guess to complete the proposition P(n) below. For each integer n > 1, let P(n) be the proposition defined as follows: 1 P(n): S(n) = E (2i – 1)(2i + 1) i=1 – iii. Prove that the proposition P(n) is true for all n 21 using a Proof by induction.

Name: Q2.Induction. For each integer n > 1, define the sum S(n) as follows:
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Description: Q2.Induction. For each integer n > 1, define the sum S(n) as follows:1111S(n) =3.5+5.71.+..+(2i — 1)(2і + 1)3(2n – 1)(2n + 1)n=11111.For example S(1) =L 2i – 1)(2i +1)and S(2) =>%3D%3D1.3(2i – 1)(2i + 1)1-33-5n=1i=1- i. Compute each of the following

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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