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Please help me on how to do these sums in mathematics, taken from the Chapter- Progressions and Series . 1.) Find sum of the series : 1.n + 2.(n-1) + 3.(n-2) +....+n.1 (Ans is: n(n+1)(n+2)/6 ) 2.) If 's' is the sum to infinity of a G.P. whose first term is 'a', then prove that the sum of the first 'n' is : [1 - (1- a/s) n ]s 3.) Series of natural numbers is divided into groups of : (1), (2,3,4) , (5,6,7,8,9),......n th group. Show that the sum of the numbers in the n th group is- n 3 + (n-1) 3

Please help me on how to do these sums in mathematics, taken from the Chapter- Progressions and Series .


1.) Find sum of the series :


  1.n + 2.(n-1) + 3.(n-2) +....+n.1


(Ans is: n(n+1)(n+2)/6 )


2.) If 's' is the sum to infinity of a G.P. whose first term is 'a', then prove that the sum of the first 'n' is :


                                    [1 - (1- a/s)n ]s


3.) Series of natural numbers is divided into groups of :


  (1), (2,3,4) , (5,6,7,8,9),......nth group.


Show that the sum of the numbers in the nth group is-


       n3 + (n-1)3


 


 

Grade:

1 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

Dear student,

This series will be like:

n(1+2+3+................)-2(1+3+5+..................)

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

Just use it.....

BEST OF LUCK...............

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