(Q). Given that
k = 1! + 2! + 3! + 4! +5! + ……….. + 120!. Then which one of the following is true
(i) k is odd
(ii) k is even
(iii) k is even or odd, can not be determined
(iv) (k+3) is even.
Solution:- Since 1! = 1 & all factorials starting from 2 till ∞ are even numbers.
Hence
& we know that odd + even = odd
Hence k is an odd number option(1)✔ Answer
now since k ia an odd number. Hence k + 3 i.e. odd + odd = even
Hence (k+3) is even number option (iv) ✔ Answer