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Verification by numerical problems
\ A + B = B + A \ A + B = B ..
\ A + B = B + A \ A + B = B ..To find the sum to infinity of a GP when the common ratio r is numerically less than 1
Consider the GP a, ar, ar 2 ... ..
Consider the GP a, ar, ar 2 ... ..Note 2:
If a and b are positive numbers, then the above method can also be applied to find the numerically greatest term in the expansion of (a - b) n..
Some Applications of Binomial Theorem for Fractional Index
If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (approximately), because x 2 , x 3 , x 4 ,. are all appr..
If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (approximately), because x 2 , x 3 , x 4 ,. are all appr..Example:
If x be numerically so small that its cube and higher powers may be neglected, then find the binomial expansions for: i) (1 + 2x) - 4 ..
If x be numerically so small that its cube and higher powers may be neglected, then find the binomial expansions for: i) (1 + 2x) - 4 ..Ratio
Ratio is the numerical relationship between two quantities of the same kind. The first quantity is called the antecedent and the second quantity is called the consequent. By performing simple operations on ratios, we get compounded ratio, duplicate ratio, triplicate ratio, sub-dupli..
Types of fractions
A Proper fraction has its numerator less than its denominator. An Improper fraction has its numerator greater than its denominator. A Mixed fraction consists of two parts, one is an integer and the other a proper fraction. Vulgar fraction is a fraction in which the..
A Proper fraction has its numerator less than its denominator. An Improper fraction has its numerator greater than its denominator. A Mixed fraction consists of two parts, one is an integer and the other a proper fraction. Vulgar fraction is a fraction in which the..Factorization of trinomials
The general form of the trinomial is (x 2 + cx + d) where c and d have different numerical values: c = a + b, and d = ab. In the given trinomial expression if all terms are positive, then both the factors are positive. If the middle term is negative, and last term is po..
Summary
Ratio is the numerical relationship between two quantities of the same kind. The first quantity is called the antecedent and the second quantity is called the consequent. By performing simple operations on ratios, we get compounded ratio, duplicate ratio, triplicate ratio, sub-duplic..
Ratio and Proportion II Summary
Summary - Ratio is the numerical relationship between two quantities of the same kind. The first quantity is called the antecedent and the second quantity is called the consequent. By performing simple operations on ratios, we get compounded ratio, duplicate ratio, triplicate ratio, sub-d..
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