Question

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

Answer 1

Correct Answer - 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.