finding the sum ..................[competitive. exam prep.... topic 7]

To find out sum of up to 10 of any multiplication table just multiply that number by 55.
Example : 
1. Sum of up to 10 of table 4 = 4 X 55 = 220
2. Sum of up to 10 of table 7 = 7 X 55 = 385
3. To find out sum of up to n of any multiplication table just multiply that number by n (n+1)/2.
Example : 
1. Sum of up to 20 of table 3 = 3 X 20 (20+1)/2 = 3 X 210 = 630
4. Sum of continuous n even numbers = n (n+1), where n= number of positions.
Example : 
1. The sum of first 5 even numbers = 2 + 4 + 6 + 8 + 10, where n = 5
The sum is = 5 (5 +1) = 5 X 6 = 30
5. Sum of continuous n odd numbers = n2 
Example : 
1. The sum of first 6 odd numbers = 1 +3 + 5 + 7 + 9 + 11, where n = 6
The sum is = (6)2 = 36
6. Sum of squares of first continuous n natural numbers = n (n +1) (2n +1)/6
Example :
1. The sum of squares of first 5 natural numbers = 12 + 22 + 32 +42 +52 where n = 5
The sum is = 5 X (5 +1) (5 X 2 +1)/6 = 5 X 6 X 11/6 = 55
7. Sum of cube of first n natural numbers = [n (n +1)/2]2
Example : 
1. The Sum of cube of first 4 natural numbers = 13 + 23+ 33+ 43 where n = 4
The sum is = [4 (4 + 1)/2]2
= [4 x 5/2]2 = (10)2 
= 100
8. If the difference of two consecutive numbers in any series is equal
= Total number/2 [ First number + Last number ]
This series is known as Parallel Series.

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