SIMPLIFICATION PART 1

Simplification , it is very important topic which covers 5-10 marks in exams. So let's discuss some mathematical terms and tricks for simplification.

1) Prime Number: A number that is divisible only by itself and 1 is called Prime number. (for ex 2,3,5,7,11.13...)

2) Natural Number: Whole numbers (positive integers) 0 to infinite are called Natural numbers.(for ex 0,1,2,3,4,5,6,...)

3) BODMAS: Bracket of Division, Multiplication, Addition and Subtraction.[ for ex: (10/2)*6+5-3]

According to this rule you must solve bracket first then divide then multiply then addition and at last subtract the number.

4) Sum of all first N natural  numbers: N(N+1)/2

For ex: 1+2+3+.....+50 = 50(50+1)/2 = 25*26 = 650

5) Sum of squares of first N natural numbers: N(N+1)(2N+1)/6

For ex: 12+22+32+……102 = 10(10+1)(2*10+1)/6 = 10*11*21/6 = 385

6) Sum of cubes of first N natural numbers: [N(N+1)/2]2

For ex: 13+23+33+……83= [8(8+1)/2]2  = (4*9)2 = 1296

7) Sum of first N odd numbers: N²

For ex: 1+3+5+7+9 = 52 =25

8) Sum of first N even numbers: N(N+1)

For ex: 2+4+6+8+10 = 5(5+1)= 5*6 = 30

9) Short tricks for square root upto infinity (addition): √x+√x+√x+√x+ …..∞ = ?

In this type of questions we break the number X in terms of n(n+1) terms and the bigger number will be the answer.

For ex: √20+√20+√20+√20 …..∞ = ?

break 20 into 4(4+1) = 4*5 = 20, so here bigger number i.e 5 will be our answer.

10) Short tricks for square root upto infinity (subtraction): √x-√x-√x-√x- …..∞ = ?

In this type of questions we break the number X in terms of n(n+1) terms and the smaller number will be the answer.

For ex: √30-√30-√30-√30 …..∞ = ?

break 30 into 5(5+1) = 5*6 = 30, so here smaller number i.e 5 will be our answer.

11) Short tricks for square root upto infinity (multiplication): √x*√x*√x*√x* …..∞ = ?

In this type of question the answer would be the number x

For ex: √12*√12*√12*√12 …..∞ = ?

here our answer will be 12.