the formula's = natural numbers. find the sum of the cubes of the first 8 natural numbers.


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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..
General Series
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 ..
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, 2, 3,} The se..
Natural Numbers
The countable numbers are called Natural Numbers. Therefore 1 is the smallest or least of all natural numbers. The highest natural number cannot be said because Natural numbers are infinite...
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 ..
Step 2:
Assume the validity of the result for n equal to some arbitrary but fixed natural number, say, ..
Whole numbers
The set of whole numbers is the set of natural numbers along with zero. so W = the set of whole numbers = 0,1,2,3,............ so Zero is the least number of the set of Whole numbers. As the whole numbers is an in..
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