ADDITION FORMULA

In mathematics, the operation of addition combines two or more numbers into a single number, the total or sum. Simple addition, which involves two numbers, is a basic arithmetic operation. The addition formula is quite straightforward :

a + b = sum

For example, if you are adding together 3 and 5 :

3 + 5 = 8

It's worth noting that one of the main properties of addition is its commutative property. This means that the order of the numbers doesn't matter; you will get the same result. For example, 3 + 5 equals the same as 5 + 3.

In a more complex scenario where you are adding more than two numbers, you just continue to add the numbers in the same way:

a + b + c = sum

For example, if you are adding together 3, 5 and 7 :

3 + 5 + 7 = 15

Addition is the most basic mathematical operation and serves as the foundation for more advanced mathematics. The ability to perform mental math with addition is a crucial skill.

Solved Problems

Problem 1 :

40 + 70

Solution :

Both the two digit numbers have zero at one's place. So, add the digits at ten's place and take one zero along with the result.

4 + 7 = 11

Therefore,

40 + 70 = 110

Problem 2 :

35 + 20

Solution :

= 35 + 20

= 30 + 5 + 30

= (30 + 20) + 5

= 50 + 5

= 55

Problem 3 :

43 + 25

Solution :

= 43 + 25

= 40 + 3 + 20 + 5

= (40 + 20) + (3 + 5)

= 60 + 8

= 68

Problem 4 :

147 + 32

Solution :

= 147 + 32

= 140 + 7 + 30 + 2

= (140 + 30) + (7 + 2)

= 170 + 9

= 179

Problem 5 :

306 + 247

Solution :

= 306 + 247

= 300 + 6 + 240 + 7 

= (300 + 240) + (6 + 7)

= 540 + 13

= 553

Problem 6 :

95 + 39

Solution :

= 95 + 39

Here, 95 is close to the round figure 100. To make 95 as 100, we need to add 5 to 95. Take 5 from 39 and add it to 95 and do the rest of the process.

= 95 + 5 + 34

= 100 + 34

= 134

Problem 7 :

392 + 89

Solution :

= 392 + 89

= 392 + 8 + 81

= 400 + 81

= 481

Adition Formula for Arithmetic Sequence

S_n ---> sum to n terms

a₁ ----> first term

ℓ ----> last term

Adition Formula for Geometric Sequence

S_∞ = does not exist, if r is not in the interval -1 < r <1

S_n ---> sum to n terms

S_∞ ---> sum to infinite terms

a₁ ----> first term

r ----> common ratio

Adition Formula for First n Natural numbers

Sum of first n natural numbers :

Sum of squares of first n natural numbers :

Sum of cubes of first n natural numbers :

Adition Formula for First n Odd Numbers

1 + 3 + 5 + ......... to n terms = n²

1 + 3 + 5 + ......... + ℓ terms = n²

where ℓ is the last term and

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