Question

For some natural N, the number of positive integral x' satisfying the equation,
1 !+2! +3! + +(x)) = (N) is:
(A) none
(B) one
(C) two
(D) infinite​

Answer 1

Answer:

• c) two

Step-by-step explanation:

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Answer 2

Answer:

1!+2!+3!+......+(x)!=(N)  

2

 is true for x=1,x=3 in that case N=1,N=3 respectively.

For, x=4, we have 1!+2!+3!+4!=33 which is not a perfect square.

Again for x≥5 1!+2!+....+(x)! is of the form 10k+3 for k is some natural number. In these cases, the given sum is not going to be a perfect square.

So, two values of x satisfies the given equation.

(C) Two is correct

Answered By

Ujjwal26200