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The greatest interger by which 1+Sigma(...

The greatest interger by which `1+Sigma_(r=1)^(30) rxxr !` is divisible is

A

composite number

B

odd number

C

divisible by 3

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
`rxxr!=(r+1-1)xxr!`
`=(r+1)!-r!`
`=V(r )-V(r-1)`
`rArrsum_(r=1)^(30)r(r!)=V(31)-V(0)=(31)!-1`
`rArr1+sum_(r=1)^(30)r(r!)=31!`
which is divisble by 31, which are prime numbers.
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