Find the sum of the first 45 natural numbers.

Given data

• We need S = 1 + 2 + … + 45.

Concept / Approach

• Use the standard formula for the sum of the first n natural numbers: S = n(n + 1)/2.

Step-by-step calculation

S = 45 × 46 / 2= 45 × 23= (40 × 23) + (5 × 23) = 920 + 115 = 1035

Verification

Pairing method: (1+45), (2+44), … gives 22 pairs of 46 plus the middle 23 ⇒ 22×46 + 23 = 1012 + 23 = 1035.

Common pitfalls

• Using n(n − 1)/2 by mistake (that is for 1 to n−1).

Final Answer

1035