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The greatest positive integer, which divides n (n + 1) (n + 2) (n + 3) for all n ∈ N is
- a)2
- b)6
- c)24
- d)120
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The greatest positive integer, which divides n (n + 1) (n + 2) (n + 3)...
Series is 30, 27, 24. 21,...
Here, a = 3o, d = -3
The maximum value is obtained when all the terms are positive.
Tn ≥ 0
30 + (n - 1) (-3) > 0
n - 1 < 10
n < 11
So, n = 10, i.e. 11th term is zero.
So, the sum is (10/2)[2(30) + 9(-3)]
= 5[60 - 27]
= 5(33)
= 165
Here, a = 3o, d = -3
The maximum value is obtained when all the terms are positive.
Tn ≥ 0
30 + (n - 1) (-3) > 0
n - 1 < 10
n < 11
So, n = 10, i.e. 11th term is zero.
So, the sum is (10/2)[2(30) + 9(-3)]
= 5[60 - 27]
= 5(33)
= 165
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The greatest positive integer, which divides n (n + 1) (n + 2) (n + 3) for all n ∈ N isa)2b)6c)24d)120Correct answer is option 'C'. Can you explain this answer?
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