MTH202 Discrete Mathematics Assignment No 02 Fall 2020 Solution / Discussion

[+ M.Tariq Malik]

MTH202 Discrete Mathematics Assignment No 02 Fall 2020 Solution / Discussion

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MTH202_2_Solution-fall-2020

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MTH202_Assignment_No_02_Solution_Fall_2020

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MTH202_Assignment_No_02_Solution_Fall_2020

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MTH202_Assignment_No_02_Solution_Fall_2020

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MTH202_Assignment_No_02_Solution_Fall_2020

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Mth 202 Solution#2 || 2021

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Assignment No.2  MTH202 (Fall 2020)

Maximum Marks: 10                      Due Date:1^st Feb, 2021

 

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Question                                                                                    Marks:10

By using Mathematical Induction prove that (n+1)!>2^(n+1) for n, where n is a positive integer greater than or equal to 4.

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MTH202 Assignment Solution 2 Fall 2020 Solution

First,  check the case

 

((4) +1)! = 120 > 32 = 2(4)+1

 

Next, we want to show that

(n+1)!>2²⁺¹

Þ (n + 2)! >

2n+2

Since (n+2)>2(n+2) for all

n ³ 4 and by hypothesis

(n + 1)!>2ⁿ⁺¹

We Get

(n+2)!=(n + 2) (n + 2)!>2.2ⁿ⁺¹

= 2n+2