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Example 14 (i) You are here
Example 14 (ii)
Example 15 Important
Example 16 Important Deleted for CBSE Board 2022 Exams
Last updated at Aug. 3, 2021 by Teachoo
Example 14 (Method 1) Find the sum of the first 1000 positive integers Positive integers start from 1 First 1000 positive integers are 1, 2, 3, 4, ………., 1000 This is an AP with First term = a = 1 Common Difference = d = 1 Number of terms = n = (1000 − 1) + 1 = 1000 To find sum, we use the formula Sum = 𝒏/𝟐[𝟐𝒂+(𝒏−𝟏)𝒅] Putting values Sum = 1000/2[2 × 1+(1000−1)(1)] Sum = 1000/2[2+999] Sum = 500 × 1001 Sum = 500500 Example 14 (Method 2) Find the sum of the first 1000 positive integers Positive integers start from 1 First 1000 positive integers are 1, 2, 3, 4, ………., 1000 This is an AP with First term = a = 1 Common Difference = d = 1 Number of terms = n = (1000 − 1) + 1 = 1000 Last term = l = 1000 To find sum, we use the formula Sum = 𝒏/𝟐[𝒂+𝒍] Putting values Sum = 1000/2[1+1000] Sum = 500 × 1001 Sum = 500500