UGC NET Questions (Paper – 1)

The sum of the first n natural numbers 1 + 2 + 3 + ... + n is known to be n(n+1)/2. This result can be derived by pairing terms from the beginning and end of the series, each pair summing to n+1, and noting that there are n/2 such pairs. It is a standard formula widely used in mathematical reasoning and aptitude questions. Hence, n(n+1)/2 is the correct expression.

Option A:
The expression n² would only match the sum for specific values of n and does not hold in general. For example, if n = 3, the sum is 6, but n² is 9, which is incorrect. Therefore, n² cannot be the correct general formula for the sum of the first n natural numbers.

Option B:
The formula n(n+1)/2 is correct because it consistently gives the right sum for all positive integers n. For instance, for n = 4, it yields 4×5/2 = 10, which equals 1+2+3+4. This formula is an essential tool for solving problems involving series and counting in UGC NET Paper 1.

Option C:
The expression n(n−1)/2 actually represents the number of ways to choose 2 items from n, that is, the combination nC2, not the sum of the first n natural numbers. While related to combinatorics, it does not correspond to the series 1+2+...+n. Thus, this option is not appropriate.

Option D:
n²/2 would give half the square of n, which again does not match the series sum in general. For example, if n = 4, n²/2 = 8, but the sum 1+2+3+4 is 10. Therefore, this expression is not valid for the sum described.