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Question

The greatest positive integer which divide $left parenthesis n plus 2 right parenthesis left parenthesis n plus 3 right parenthesis left parenthesis n plus 4 right parenthesis left parenthesis n plus 5 right parenthesis left parenthesis n plus 6 right parenthesis text if end text n element of N$ is

4
24
120
240

The correct answer is: 120

Related Questions to study

The sets $S subscript 1 comma S subscript 2 comma S subscript 3 comma horizontal ellipsis horizontal ellipsis$ are given by $S subscript 1 equals open parentheses 2 over 1 close parentheses comma S subscript 2 equals open parentheses 3 over 2 comma 7 over 2 close parentheses comma S subscript 3 equals open parentheses 4 over 3 comma 9 over 3 comma 14 over 3 close parentheses S subscript 4 equals open parentheses 5 over 4 comma 11 over 4 comma 17 over 4 comma 23 over 4 close parentheses horizontal ellipsis horizontal ellipsis$ then the sum of numbers in the set $S subscript 20$ is :

The sets $S subscript 1 comma S subscript 2 comma S subscript 3 comma horizontal ellipsis horizontal ellipsis$ are given by $S subscript 1 equals open parentheses 2 over 1 close parentheses comma S subscript 2 equals open parentheses 3 over 2 comma 7 over 2 close parentheses comma S subscript 3 equals open parentheses 4 over 3 comma 9 over 3 comma 14 over 3 close parentheses S subscript 4 equals open parentheses 5 over 4 comma 11 over 4 comma 17 over 4 comma 23 over 4 close parentheses horizontal ellipsis horizontal ellipsis$ then the sum of numbers in the set $S subscript 20$ is :

If $S subscript 1 equals left curly bracket 1 right curly bracket comma S subscript 2 equals left curly bracket 2 comma 4 right curly bracket comma S subscript 3 equals left curly bracket 3 comma 6 comma 9 right curly bracket S subscript 4 equals left curly bracket 4 comma 8 comma 12 comma 16 right curly bracket comma horizontal ellipsis horizontal ellipsis$
then sum of the numbers in the set is

If $S subscript 1 equals left curly bracket 1 right curly bracket comma S subscript 2 equals left curly bracket 2 comma 4 right curly bracket comma S subscript 3 equals left curly bracket 3 comma 6 comma 9 right curly bracket S subscript 4 equals left curly bracket 4 comma 8 comma 12 comma 16 right curly bracket comma horizontal ellipsis horizontal ellipsis$
then sum of the numbers in the set is

If $n$ is even, $S subscript n equals 1 squared plus 2.2 squared plus 3 squared plus 2.4 squared plus 5 squared plus 2.6 squared horizontal ellipsis n$ terms $equals fraction numerator n left parenthesis n plus 1 right parenthesis squared over denominator 2 end fraction$ , if $straight n$ is odd then $S subscript n equals$

If $n$ is even, $S subscript n equals 1 squared plus 2.2 squared plus 3 squared plus 2.4 squared plus 5 squared plus 2.6 squared horizontal ellipsis n$ terms $equals fraction numerator n left parenthesis n plus 1 right parenthesis squared over denominator 2 end fraction$ , if $straight n$ is odd then $S subscript n equals$

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