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Questions 10 complete with a sollution required for the question above .. .

Questions 10 complete with a sollution required for the question above .. .

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1 Answers

Arun
25763 Points
3 years ago
Dear Pushkar
 
when n = 0 the quotient = 1 
when n = 1 the quotient = 3!/3! = 1 
assuming it's true when n = k 
when n = k+1 
(3k+3)(3k+2)(3k+1)*(3k)!/((3!)^n (3!)) = (3k)!/(3!)^k * (3k+3)(3k+2)(3k+1)/3! = X * (k+1) * (3k+2)(3k+1)/2 
X is integer, (3k+2) (3k+1) are two consecutive integers so one must be even, therefore the result is an integer

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