Questions 10 complete with a sollution required for the question above .. .
pushkar , 6 Years ago
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9 grade maths> Questions 10 complete with a sollution re...
1 Answers
Arun
Last Activity: 6 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
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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