{n(n+1)/2 : n is a positive integer} isa)a finite setb)an infinite setc)is an empty setd)none of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Explanation:
The given set is {n(n+1)/2 : n is a positive integer}.
To determine whether the given set is finite or infinite, we need to understand the pattern of the set.

Let's list out the first few terms of the set:

n = 1: 1(1+1)/2 = 1
n = 2: 2(2+1)/2 = 3
n = 3: 3(3+1)/2 = 6
n = 4: 4(4+1)/2 = 10
n = 5: 5(5+1)/2 = 15

From the above list, we can observe that the set is increasing and contains all the integers of the form n(n+1)/2.

Hence, the given set is an infinite set.

Answer

Infinite set you can check it by putting values in n

Answer

1) whatever N is.. if 1 is added to it the resulting number divisible by 2 this is possible cause interger is infinite
2) no matter what is in bracket ..there is one sequence showing first adding then multiply and last divide by two so coming interger is an infinite set

Answer

The answer will be an infinite set because the set from which we have taken the values of n, is itself an infinite set i.e, The set of postive integers is an infinite set.

Answer

- The set {n(n+1)/2 : n is a positive integer} represents triangular numbers.
- Each triangular number is generated by summing the first n natural numbers: (1, 3, 6, 10, 15, ...).
- As n increases, new triangular numbers can be formed indefinitely.
- There is no upper limit to the value of n, meaning the process can continue forever.
- Thus, the set is infinite.
- Correct answer: B, an infinite set.

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