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Addition and Subtraction

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Addition

Addition is a mathematical operation to combine two or more numbers/objects.

Example : ‘‘2 marbles and 3 marbles make 5 marbles,’’ you can write 2 + 3 = 5 on the board or on paper.

Formulae Related to Sum of Numbers

1. Sum of first n natural numbers

$\mathbf{\frac{1}{2}n(n+1)}$

2. Sum of first n even numbers

$\mathbf{n(n+1)}$

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3. Sum of first n odd numbers

$\mathbf{n^{2}}$

4. Sum of even numbers from 1 to n

$\mathbf{\frac{n}{2}\left(\frac{n}{2}+1\right)}$

5. Sum of odd numbers from 1 to n

$\mathbf{\left(\frac{n+1}{2}\right)^{2}}$

6. Sum of squares of first n natural numbers

$\mathbf{\frac{1}{6}n(n+1)(2n+1)}$

7. Sum of cubes of first n natural numbers

$\mathbf{\left\{\frac{1}{2}n(n+1)\right\}^{2}}$

Example

Q. Find the sum of all natural numbers between 11 to 30 included them.

a. 380	b. 410
c. 400	d. 430

Q. Find the sum of odd numbers from 1 to 31.

341
321
256
248

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