Tricks - Sum Of Natural, Even, Odd Numbers

Additional reference for Finding square quickly

Tricks for:
1)Sum of first n Natural numbers
2)Sum of first n Even numbers
3)Sum of first n Odd numbers

1)Sum of first n Natural numbers

1 : 1 = 1 1 : 1 (1*2)/2 = 1
2 : 1 +2= 3 2 : 3 (2*3)/2 = 3
3 : 1+ 2 +3 = 6 3 : 6 (3*4)/2 = 6
4 : 1+2+3+4 = 10 4 : 10 (4*5)/2 = 10
5 : 1+2+3+4+5 = 15 5 : 15 (5*6)/2 = 15

n * (n+1)
----------
2

Sum of first 50 Natural numbers

n * (n+1)
----------
2

50 * (50+1) 25 * 51 = 1275
---------- =
2

Sum of first 100 Natural numbers

n * (n+1)
----------
2

100 * (100+1) 50 * 101 = 5050
------------- =
2

2)Sum of first n Even numbers

1: 2 = 2 1 : 2 1*2 = 2
2: 2+4 = 6 2 : 6 2*3 = 6
3: 2 + 4 + 6 = 12 3 : 12 3*4 = 12
4: 2+4+6+8 = 20 4 : 20 4*5 = 20
5: 2+4 +6 +8 +10= 30 5 : 30 5*6 = 30

n * (n+1)

Sum of first 50 Even numbers
n * (n+1)
50 * 51 = 2550

Sum of first 100 Even numbers
n * (n+1)
100 * 101 = 10100

3)Sum of first n Odd numbers

1: 1= 1 1 : 1 1^2 = 1
2: 1+ 3 = 4 2 : 4 2^2 = 4
3: 1+3+5 =9 3 : 9 3^2 = 9
4: 1+3+5+7= 16 4 : 16 4^2 = 16
5: 1+3+5+7+9= 25 5 : 25 5^2 = 25

n^2

Sum of first 50 Odd numbers
n^2
50^2 = 2500

Sum of first 100 Odd numbers
n^2
100^2 = 10000

[RupKshatri]

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