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Numbers

 

 

Important formulae and tricks and shortcuts of Numbers:

We are providing you Important Concepts and Tricks on Numbers which are usually asked in almost all competitive exams like IBPS, Govt. Exams and CAT and in quantitative aptitude of MNCs. Use these below given tricks to solve questions within minimum time. These tricks will be very helpful for your upcoming Competitive Exam.

 

1. Number Sets   

a. Counting Numbers (Natural numbers)

1, 2, 3 ...

b. Whole Numbers

0, 1, 2, 3 ...

c. Integers

-3, -2, -1, 0, 1, 2, 3 ...

d. Rational Numbers

Rational numbers can be expressed as ab/ab where a and b are integers and b≠0b≠0
Examples: 112/112, 42/42, 00, −8/11−8/11 etc.

All integers, fractions and terminating or recurring decimals are rational numbers.

 

Formulas of Number Series

  1. 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
  2. (12 + 22 + 32 + ..... + n2) = n ( n + 1 ) (2n + 1) / 6
  3. (13 + 23 + 33 + ..... + n3) = (n(n + 1)/ 2)2
  4. Sum of first n odd numbers = n2
  5. Sum of first n even numbers = n (n + 1)

Mathematical Formulas

 

Shortcuts for number divisibility check

 

For solved problems on above formulas please visit below sections: