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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Assignment No.2 MTH202 (Fall 2020)
Maximum Marks: 10 Due Date:1^{st} Feb, 2021
DON’T MISS THESE: Important instructions before attempting the solution of this assignment:
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.
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)!>2^{2}^{+1}
Þ (n + 2)! >
2n+2
Since (n+2)>2(n+2) for all
n ³ 4 and by hypothesis
(n + 1)!>2^{n}^{+1}
We Get
(n+2)!=(n + 2) (n + 2)!>2.2^{n}^{+1}
= 2n+2
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