General Series
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..
Binomial Theorem Summary
of (a + b) n and is given by - If n is an odd natural number, then there are two middle terms in the expansion of (a + b)n and are given by i) The sum of all binomial coefficients in the expansion of (1+x) n is 2 n . ii) The sum of all even binomial..
of (a + b) n and is given by - If n is an odd natural number, then there are two middle terms in the expansion of (a + b)n and are given by i) The sum of all binomial coefficients in the expansion of (1+x) n is 2 n . ii) The sum of all even binomial..Suggested answer:
3. To find the sum to the cubes of first n natural numbers. ..
3. To find the sum to the cubes of first n natural numbers. ..General Series
1. To find the sum of first n natural numbers. ..
1. To find the sum of first n natural numbers. ..Sequences and Series
Sequence : A set of numbers arranged in a definite order according to some definite rule is called a sequence.A sequence is a function whose domain is the set N of natural numbers. Series : Indicated sum of the terms in a sequence is called a ..
Number Theory - Test Questions
Question 1 - 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 ..
Question 1 - 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 ..Rational and Irrational Numbers Introduction
Introduction - The sets of numbers which every student must remember are: The set of natural numbers N = {1, 2, 3, 4, 5, } The set of whole numbers W = {0, 1, 2, 3, 4, 5,} The set of integers Z = I = {, -3, -2, -1, 0, 1..
Introduction - The sets of numbers which every student must remember are: The set of natural numbers N = {1, 2, 3, 4, 5, } The set of whole numbers W = {0, 1, 2, 3, 4, 5,} The set of integers Z = I = {, -3, -2, -1, 0, 1..Question 2
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 are infinite numb..
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 are infinite numb..Question 8
Question: Find three numbers in AP whose sum is 33 and whose product is 1155. Answer: Let a - d, a, a + d be the three numbers in AP. The numbers are ..
Question: Find three numbers in AP whose sum is 33 and whose product is 1155. Answer: Let a - d, a, a + d be the three numbers in AP. The numbers are ..Step 2:
Assume the validity of the result for n equal to some arbitrary but fixed natural number, say, ..
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