Question 17 of 51beginner💡 UnderstandEssay1 mark

Can the same approach be used to find the sum of 1+2+3+…+1001 + 2 + 3 + \ldots + 100?

Correct Answer

Yes, the same approach can be used. The method of writing the sum from 1 to 100, reversing it, and adding the two expressions works for any value of n. This leads to the general formula for the sum of the first n natural numbers: S_n = n(n+1)/2. Substituting n = 100, the sum is S_100 = 100(101)/2 = 5050.

Exercise: Think and Reflect | Q: 1 | (Chapter: 11)
For More Understanding

Explanation

The textbook explains that the method of writing the sum, reversing it, and adding the two expressions can be used to arrive at the formula for the sum of the first n natural numbers for any value of n. By applying the derived formula S_n = n(n+1)/2 with n=100, we can easily find the sum without adding all the numbers individually.

Solution Steps

  1. Step 1: State that the approach of writing the sum, reversing it, and adding works for any value of n.

  2. Step 2: Apply the general formula for the sum of the first n natural numbers, S_n = n(n+1)/2.

  3. Step 3: Substitute n = 100 into the formula: S_100 = 100(101)/2.

  4. Step 4: Calculate the final sum: S_100 = 5050.

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