Correct Answer - Option 4 : A rational number
Concept:
- A number r is called a rational number, if it can be written in the form p/q, where p and q are integers and q ≠ 0.
- The decimal expansion of a rational number is either terminating or non-terminating recurring.
- All the rational and irrational numbers make up the collection of real numbers.
Calculation:
Let \(x =n^7 + \dfrac{n^5}{5} + \dfrac{2n^3}{3} - \dfrac{n}{105}\)
Where n = any positive integer
Let's take n = 1
⇒ \(x =1^7 + \dfrac{1^5}{5} + \dfrac{2\times 1^3}{3} - \dfrac{1}{105}\)
\(\Rightarrow x =1 + \dfrac{1}{5} + \dfrac{2}{3} - \dfrac{1}{105}\)
\(\Rightarrow x = \dfrac{13}{7}\)
We can see that x is a rational number & from the above options, it is clear that, only option 4 belongs to the category of x.