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 fir..
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 i..
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 i..Summary
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 obt..
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 obt..Examples:
1. Find the sum to the series 1+2x+3x 2 +.... to n terms and to infinity when x < 1..
General Series
1. To find the sum of first n natural numbers. ..
1. To find the sum of first n natural numbers. ..Summary
) ka, kb, kc are in G.P. (b) a/k, b/k, c/k are in G.P. (x) (a) If the product of three numbers in G.P. is given, then the numbers should be taken as a/r, a, ar. (b) If the product of four numbers in G.P. is given, then the numbers should be taken as a/r 3 , a..
) ka, kb, kc are in G.P. (b) a/k, b/k, c/k are in G.P. (x) (a) If the product of three numbers in G.P. is given, then the numbers should be taken as a/r, a, ar. (b) If the product of four numbers in G.P. is given, then the numbers should be taken as a/r 3 , a..Introduction
A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For example, x - y, a + 3b, x 3 + 4y etc. are binomials. We know that, For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical..
A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For example, x - y, a + 3b, x 3 + 4y etc. are binomials. We know that, For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical..Suggested answer:
4. Sum the following: i) 1.2 + 2.4 + 3.8 +.... to n ter..
4. Sum the following: i) 1.2 + 2.4 + 3.8 +.... to n ter..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 +..
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 +..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..
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