1. 1+2+3+4…. +n = n (n+1) / 2

2. 12+22+32…. +n2 = n (n+1)(2n+1) / 6

3. 13+23…+n3 = [n2(n+1)2] / 4

4. 1+3+5…. 2n-1= n2

5. Every prime number greater than 3 can be written using the formula (6k+1) or (6k-1)

6. Number of factors present in a number is given as (p+1)(q+1)(r+1)… Where N=(ap)+(bq)+(cr)… Where a, b, c are prime numbers and p, q, r are positive numbers In the same way sum of all factors=[(a(p+1) / (a-1)][(b(q+1) / (b-1)]…

7. If there is P volume of pure liquid initially in each operation and Q volume is taken out and replaced by Q volume of water then at the end of n such operations, the concentration k is given as K = [(P-Q) / P]n

8. If successive increase in percentage is given p%, q%, r% then effective % increase is given as [(100+p)/100][(100+q)/100][(100+r)/100]-1}*100

9. If an article is sold such that a article has a profit of p% on one and loss of p% on other then we have the net result to be loss and the loss percent is (p2) / 100