Factorial & Binomial Coefficient
1. Define n! factorial and binomial coefficient:
Solution:
2.Simplify:
Solution:
3.Solve in positive integers:
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4.Solve in positive integers:
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5.Solve in integers:
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6.Which number is greater?
a = 50! + 53! or b = 51! + 52!
Solution:
a) 50! + 53! = 50! + 53.52.51.50! = 50!(1 +53.52.51)
b) 51! +52! = 51! + 52.51!= 51!(1+52 ) = 51!.53 = 51.50!.53 = 50!.51.53
Pretože 50!.(1 +53.52.51) > 50!.53.51
1+53.52.51> 53.51
Stands:: a > b
7.Solve in positive integers:
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8.Solve in positive integers:
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9.Solve the set of equations in positive integers and non-negative integers:
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10.For which positive integer x stands:
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