Home
Class 12
MATHS
The series of natural numbers is divided...

The series of natural numbers is divided into groups`:(1);(2,3,4);(5,6,7,8,9)...` and so on. The sum of numbers in the `n^(th)` group is

Text Solution

AI Generated Solution

To find the sum of the numbers in the \( n^{th} \) group of the series of natural numbers divided into groups as described, we can follow these steps: ### Step 1: Identify the Number of Terms in Each Group The groups are structured as follows: - 1st group: (1) → 1 term - 2nd group: (2, 3, 4) → 3 terms - 3rd group: (5, 6, 7, 8, 9) → 5 terms - 4th group: (10, 11, 12, 13, 14, 15, 16) → 7 terms ...
Promotional Banner

Topper's Solved these Questions

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Do yourself|3 Videos

  • SEQUENCE AND PROGRESSION

    ALLEN|Exercise Do yourself 2|2 Videos

  • RACE

    ALLEN|Exercise Race 21|14 Videos

  • TEST PAPER

    ALLEN|Exercise CHEMISTRY SECTION-II|3 Videos

Similar Questions

Explore conceptually related problems

The sequence of odd natural numbers is divided into groups 1,3,5,7,9,11,"…." and so on. Show that the sum of the numbers in nth group is n^(3) .

The series of natural numbers is divided into grounds as (1), (2, 3, 4), (3, 4, 5, 6, 7), (4, 5, 6, 7, 8, 9, 10)………. If sum of elements in the 20^(th) ground is l , then l is equal to

A series is given in the form (1) + (2+3+4)+ (5+6+7+8+9)+..... Find the sum of the numbers in the rth bracket.

The sequence N of natural numbers is divided into classes as follows. Show that the sum of the numbers in nth row is (2n^2+1)

The cubes of the natural numbers are grouped as 1^(3),(2^(3),3^(3)),(4^(3),5^(3),6^(3)), . . . . . . . ., the the sum of the number in the n^(th) group, is

The natural numbers are grouped as follows : (1),(2,3) , (4,5,6), (7,8,9,10), ... Find an expression for the first term of the nth group.

Natural numbers have been divided into groups in the following way: 91,3),(5,7,9,11),(13,15,….,23),…….. Show that the sum of numbers in the nth group is 4n^3

Natural numbers are written as 1, (2,3), (4,5,6).. Show that the sum of number in the nth group is (n)/(2) (n +1) .

The sum of n natural numbers is 5n^2+4n . Find the 8th term.

The number of different ways in which the first twelve natural numbers can be divided into three groups, each having four elements, such that the numbers in each group are in arithmetic progression is