Mathematics · Arithmetic Progressions · NCERT Examples
Example 14
A complete, independently verified solution for NCERT Example 14.
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Mathematics · Chapter 5 · NCERT Examples
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NCERT Example
Example 14
Find (i) the sum of the first 1000 positive integers and (ii) the sum of the first n positive integers.
Solution
Board-exam working:
The positive integers form an AP with a=1,d=1.
Use Sₙ=n(a+l)/2.
(i) Here n=1000 and l=1000.
S₁₀₀₀=1000/2(1+1000)=500×1001=500500.
(ii) For the first n positive integers, l=n.
Therefore Sₙ=n/2(1+n)=n(n+1)/2.
Final answer
(i) 500500; (ii) n(n+1)/2.