Some Observations
For n N, in the expansion of (a + b) n , we observe that: the number of terms is n+1 the exponent of 'a' decreases from n to 0 the exponent of 'b' increases from 0 to n the sum of exponents of 'a' and 'b' in any term is n. the coefficient of any term is n C k where k is..
For n N, in the expansion of (a + b) n , we observe that: the number of terms is n+1 the exponent of 'a' decreases from n to 0 the exponent of 'b' increases from 0 to n the sum of exponents of 'a' and 'b' in any term is n. the coefficient of any term is n C k where k is..Comparison of decimal numbers
1.65; 1.95; 1.65 Observe the digit in the units pace.They are same. Observe the decimal numbers.The biggest decimal number is 9 Therefore 1.95 is the greatest. Now observe 1.68 and 1.65.Here the digit in the unit place is same.The digit of the tenth pace is aso th..
Introduction
The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical Induction ..
Mathematical Induction
Introduction - The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical In..
Study the following examples
1. The numbers 2, 3, 5 and 8. 2. The solutions of the equation x 2 - 2x - 15 = 0. 3. The letters of the word "Chase". 4. People living in our locality. 5. The students Mary, Hillary, Catherine. 6. The workers who are absent from the factory. 7. The capital cities of Asia. 8. The positive even int..
Identities or Properties of Logorithms
Properties of logarithm - 1.log a mn= log a m+log a n. 2. log a (m/n) = log a m- log a n. 3. log a m n = n log a m. 4. log a b = log e b/log e a It can be observed some interesting facts. log a a=1 log a 1=0. log a b= 1/log b a. log a (1/x)= - log a ..
Factorisation using Identities
Factorisation using Identities - Recall the following identities for finding the products: Observe that the LHS in the identities are all factors and the RHS are their products. Thus, we can write the factors as follow..
Factorisation using Identities - Recall the following identities for finding the products: Observe that the LHS in the identities are all factors and the RHS are their products. Thus, we can write the factors as follow..Suggested answer:
Identify the HCF of the terms of the groups. Now, observe that, (2x - 3a) is a common factor for both the groups. Therefore (2x - 3a) is one of the factors of the given expression. The other factor is identified by dividing each group by the common factor i.e. (2x - 3a). ..
Identify the HCF of the terms of the groups. Now, observe that, (2x - 3a) is a common factor for both the groups. Therefore (2x - 3a) is one of the factors of the given expression. The other factor is identified by dividing each group by the common factor i.e. (2x - 3a). ..Examples:
Each one of the following series form an A.P. i) 1, 3, 5, 7, ii) 3, 7, 11, 15, iii) 15, 12, 9, iv) x, x - d, x - 2d, ..... The common difference is found by subtracting any term of the series from the immediate succeeding term. In the above example, common difference in the first is 2, in the..
Each one of the following series form an A.P. i) 1, 3, 5, 7, ii) 3, 7, 11, 15, iii) 15, 12, 9, iv) x, x - d, x - 2d, ..... The common difference is found by subtracting any term of the series from the immediate succeeding term. In the above example, common difference in the first is 2, in the..Mathematical Induction Introduction
Introduction - The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical In..
Introduction - The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical In..See what our Users say :
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