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If P(n) : (5n)/2 is less than n!, n belongs to Natural numbers, then P(n) is true for n1. greater than 22. All greater than 33. All less than 44. None of these |
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Answer» Correct Answer - Option 2 : All greater than 3 Given: P(n) : 5n/2 < n! n belongs to Natural number Calculation: P(n) : (5n)/2 < n! Put n = 1, 2, 3 ,4, ...... For n = 1 P(1) : 5(1)/2 > 1! = 2 > 1 (false) For n = 2 P(2) : 5(2)/2 > 2! = 5 > 2 (false) For n = 3 P(3) : 5(3)/2 > 3! = 7.5 > 6 (false) For n = 4 P(4) : 5(4)/2 > 4! = 10 < 24 (True) similarly for P(5) ,P(6).... and for all n natural numbers it is true ∴ P(n) is true for n all greater than 3 |
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