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Question

Greatest integer by which $1 plus not stretchy sum from r equals 1 to 30 of r cross times r factorial$ is divisible is

Composite number
Odd number
Divisible by 3
None of these

The correct answer is: None of these

$cross times r factorial equals open parentheses r plus 1 minus 1 close parentheses cross times r factorial$
$equals open parentheses r plus 1 close parentheses factorial minus r factorial$
$equals V open parentheses r close parentheses minus V left parenthesis r minus 1 right parenthesis$
$rightwards double arrow blank not stretchy sum from r equals 1 to 30 of r open parentheses r factorial close parentheses equals V open parentheses 31 close parentheses minus V open parentheses 0 close parentheses$
$rightwards double arrow 1 plus not stretchy sum from r equals 1 to 30 of r left parenthesis r factorial right parenthesis equals 31 factorial$
Which is divisible by 31 consecutive integers which is a prime number

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