Difference between the sum of the first 100 natural numbers and the sum of the first 100 whole numbers
Answers
Answer:
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The difference between the sum of the first hundred natural numbers and the sum of the first hundred whole numbers is 100.
Given:
The first hundred natural numbers and whole numbers.
To Find:
The difference between the sum of the first hundred natural numbers and the sum of the first hundred whole numbers.
Solution:
Natural numbers are also called cardinal numbers since they are used for ordering and counting.
Whole numbers are natural numbers along with 0.
The first hundred natural numbers are 1,2,3,...100.
The sum of the first hundred natural numbers = 1+2+3+...100
The first hundred natural numbers are 0,1,2,3,...99.
The sum of the first hundred natural numbers = 0+1+2+3+...99.
The difference between the sum of the first hundred natural numbers and the sum of the first hundred whole numbers is
= (1+2+3+...100)-(0+1+2+3+...99)
On rearranging the terms, we have
The difference between the sum of the first hundred natural numbers and the sum of the first hundred whole numbers
= (1-1)+(2-2)+(3-3)+.....(99-99)+(100-0)
= 0+0+...+100 = 100.
Hence the difference between the sum of the first hundred natural numbers and the sum of the first hundred whole numbers is 100.
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