SSC Tricks for mathematical series

“Series” another an important chapter which I want to discuss with my readers/ students. This discussion will help you a lot in understanding the various kinds of mathematical series. There are mainly six types of series which are mainly and frequently asked in the competition examinations, which are as follows :-

Ø  Natural number series. Eg. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ……………………….

Ø  Even natural numbers series. Eg. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ………….

Ø  Odd natural numbers series. Eg. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, ……………

Ø  Square of natural number series. Eg. 1², 2², 3², 4², 5², ……………………….

Ø  Cube of natural numbers series. Eg. 1³, 2³, 3³, 4³, 5³, ………………………..

Ø  Miscellaneous series.

SERIES 1^st :-   
Natural Number Series :- 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …………….

Sum of n- natural numbers → 1 + 2 + 3 + 4 + 5 + 6 + 7 + ………. n terms

                                        Sum of n- natural numbers =  n (n+ 1)  

                                                                                                   2

                                            Where n= number of terms in the given series

Condition :- The above formula is applicable only and only if the series starts from 1.

SERIES 2^nd :- 
Even Natural Number Series :- 2, 4, 6, 8, 10, 12, 14,  …………….

Sum of n- even natural numbers → 2 + 4 + 6 + 8 + 10  ………. n terms

Sum of n- even natural numbers = n (n+1)

                                                              Where n= number of terms in the given series

                                                     n = last term /2

Condition :- The above formula is applicable only and only if the series starts from 2.

SERIES 3^rd  :- 
Odd Natural Number Series :- 1, 3, 5, 7, 9, 11, 13, 15,  ……………. 
 Sum of n- odd natural numbers → 1 + 3 + 5 + 7 + 9 +  ………. n terms

 Sum of n- odd natural numbers = n²

                                                              Where n= number of terms in the given series

                                                  n = (last term + 1) / 2

Condition :- The above formula is applicable only and only if the series starts from 1.

SERIES 4^th  :- 
Square of Natural Number Series :- 1², 2², 3², 4², 5², 6², 7², 8²,  …………….

Sum of squares n- natural numbers → 1² + 2² + 3² + 4² + 5² + 6² ………. n terms

Sum of squares n- natural numbers = 1/6 [ n (n+1) (2n+1)]

                                                              Where n= number of terms in the given series

            Condition :- The above formula is applicable only and only if the series starts from 1.

SERIES 5^th  :-
Cube of  Natural Number Series :- 1³, 2³, 3³, 4³, 5³, 6³, 7³, 8³, …………….

Sum of cubes of n- natural numbers → 1³ + 2³ + 3³ + 4³ + 5³ + 6³  ………. n terms

Sum of n- natural numbers =[ n (n+1)/2]²

Where n= number of terms in the given series

Condition :- The above formula is applicable only and only if the series starts from 1.