Find the sum of first 1000 positive integers.

1.	Find the sum of first 1000 positive integers.
Answer» Given A.P. 1, 2, 3, 4, 5 …….. 1000 First term (a) = 1 Common difference (d) = 2 – 1 = 1 Last term (l) = 1000 Formula, S_n = n/2(a + l) S₁₀₀₀ = 1000/2 (1 + 1000) = 500 × 1001 = 500500 Hence, sum of first 1000 positive integers. = 500500

Answer»

Given A.P.

1, 2, 3, 4, 5 …….. 1000

First term (a) = 1

Common difference (d) = 2 – 1 = 1

Last term (l) = 1000

Formula, S_n = n/2(a + l)

S₁₀₀₀ = 1000/2 (1 + 1000)

= 500 × 1001 = 500500

Hence, sum of first 1000 positive integers.

= 500500

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