NCERT Class X Chapter 5: Arithmetic Progression Example 14(ii)
NCERT Class X Chapter 5: Arithmetic Progression Example 14(ii) Question: Find the sum of : the first n positive integers Given: A positive integer n To Find: The sum of the first n positive integers: 1 + 2 + 3 + ... + n Formula: The sum S of the first n positive integers is given by the formula: S = n(n + 1) 2 Solution: Let S be the sum of the first n positive integers. S = 1 + 2 + 3 + ... + (n - 1) + n We can also write the sum in reverse order: S = n + (n - 1) + (n - 2) + ... + 2 + 1 Adding the two equations, we get: 2S = (1 + n) + (2 + n - 1) + (3 + n - 2) + ... + (n - 1 + 2) + (n + 1) 2S = (n + 1) + (n + 1) + (n + 1) + ... + (n + 1) (n times) Therefore, 2S = n(n + 1) ⇒ S = n(n + 1) 2 Result: The sum of the first n positive integers is n(n + 1) 2 Next question solution: NCERT Class X Chapter 5: Arithmetic Progression Example 15 Explore more in Arithmetic Progressions chapter: Click this link ...