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Question
The sum of first n natural numbers is given by `1/2n^2 + 1/2n`. Find the sum of natural numbers from 11 to 30.
Solution
Given, sum of first n natural numbers = `1/2n^2 + 1/2n`
Sum of natural numbers from 11 to 30 = Sum of first 30 natural numbers – Sum of first 10 natural numbers
= `[1/2(30)^2 + 1/2(30)] - [1/2(10)2 + 1/2(10)]`
= `900/2 + 30/2 - 100/2 - 10/2` ......[Divide each term by 2]
= 450 + 15 – 50 – 5
= 410
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