the sum of the three consecutive natural numbers lies between 66 and 81. find the smallest and largest possible numbers.

1. To find the sum of first n natural numbers. 2. To find the sum to squares of first n natural numbers. 3. To find the sum to the cubes of first n natural nu..

Question: Show that the sum of the cubes of any number of consecutive integers is divisible by the sum of those integers. Answer: Let the consecutive integers be (n + 1), (n + 2), (n + 3),....,(n + m) Sum of the cubes..

) It is not possible to find the exact value of an irrational number. (iii) All rational and irrational numbers can be marked on the number line. Write two possible irrational numbers between 2 and 3. Consider the squar..

Sigma Notation - The Greek letter S (read as sigma) denotes the sum. When written before the n t h term of series, implies, the sum of all terms obtained by giving to n the different values 1,2,3n. Thu..

Question: List the elements of the following sets and specify whether they are finite or infinite: Answer: (i) Since there is no natural number lying between 2 and 3, the set is a null set i.e. f . This is a finite set. (i) Since there ar..

is called unit matrix or identity matrix. A x I = A = I x A. If . Find (i) A(BC), (ii)(AB)C. Is A(BC) = ..

The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determinants obtained from D by replacing respectively t..

The sum of the three consecutive natural numbers lies between 66 and 81. Find the smallest and largest possible numbers. => Smallest: 22 and Largest: 26 or ..

Identify the largest number. => 9.61 × 10 2 or 9.21 × 10 4 or 9.81 × 10 3 or 9.41 × 10 4..

Identify the largest number. => 9.21 × 10 4 or 9.81 × 10 3 or 9.61 × 10 2 or 9.41 × 10 4..