Higher Algebra: A Sequel to Elementary Algebra for SchoolsMacmillan, 1891 - 557 páginas |
Dentro del libro
Resultados 1-5 de 44
Página xv
... taking x small enough , any term of the series a + a1x + a2x2 + ... .. may be made as large as we please compared with the sum of all that follow it ; and by taking a large enough , any term may be made as large as we please compared ...
... taking x small enough , any term of the series a + a1x + a2x2 + ... .. may be made as large as we please compared with the sum of all that follow it ; and by taking a large enough , any term may be made as large as we please compared ...
Página xvii
... taking any convergent for the continued fraction 279 Each convergent is nearer to the continued fraction than a fraction with smaller denominator pp ' > or < x2 , according as P p ' > or < qq ' Examples XXV . b . 280 281 281 CHAPTER ...
... taking any convergent for the continued fraction 279 Each convergent is nearer to the continued fraction than a fraction with smaller denominator pp ' > or < x2 , according as P p ' > or < qq ' Examples XXV . b . 280 281 281 CHAPTER ...
Página 3
... taking the same quantity from both its terms . 12. When two or more ratios are equal many useful pro- positions may be proved by introducing a single symbol to denote each of the equal ratios . The proof of the following important ...
... taking the same quantity from both its terms . 12. When two or more ratios are equal many useful pro- positions may be proved by introducing a single symbol to denote each of the equal ratios . The proof of the following important ...
Página 40
... taking a sufficient number of terms the sum can be made to differ by as little as we please from 2 . In the next article a more general case is discussed . 57. From Art . 55 we have s = a ( 1- " ) 1 - r ar " а 1 γ 1 -r Suppose is a ...
... taking a sufficient number of terms the sum can be made to differ by as little as we please from 2 . In the next article a more general case is discussed . 57. From Art . 55 we have s = a ( 1- " ) 1 - r ar " а 1 γ 1 -r Suppose is a ...
Página 44
... taking n sufficiently great . In this case , assuming that all the terms which involve rn can be made so small that they may be neglected , we obtain α dr + 1 − r * ( 1 − r ) 2 - - for the sum to infinity . We shall refer to this ...
... taking n sufficiently great . In this case , assuming that all the terms which involve rn can be made so small that they may be neglected , we obtain α dr + 1 − r * ( 1 − r ) 2 - - for the sum to infinity . We shall refer to this ...
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Otras ediciones - Ver todas
Higher Algebra: A Sequel to Elementary Algebra for Schools H. S. Hall,S. R. Knight Sin vista previa disponible - 2017 |
Higher Algebra: A Sequel to Elementary Algebra for Schools (Classic Reprint) H. S. Hall Sin vista previa disponible - 2017 |
Higher Algebra: A Sequel to Elementary Algebra for Schools H. S. Hall,S. R. Knight Sin vista previa disponible - 2018 |
Términos y frases comunes
a+b+c a₁ Algebra annuity arithmetic mean arithmetical progression ax² b₁ balls Binomial Theorem C₁ C₂ CAMB COLL common difference common ratio complete quotient contains continued fraction decimal denominator denote digits divided divisible equal event Example expansion expression factors find the chance find the number Find the sum find the value finite geometric Geometrical Progression given series greater harmonic means hence In+1 infinite series less letters logarithms multiplying negative nth term number of shot number of solutions number of terms obtain P₁ partial fractions positive integers preceding article prime number proper fraction prove quadratic quadratic equation quantities radix recurring decimal result scale of relation series is convergent shew shillings Similarly Solve the equations suppose U₁ U₂ unity varies whence zero
Pasajes populares
Página 55 - ... any number divided by 9 will leave the same remainder as the sum of its digits divided by 9.
Página 169 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Página 111 - The number of combinations of n things г at a time is equal to the number of combinations of n things n—r at a time.
Página 488 - At the 50th mile stone from London, A overtook a drove of geese which were proceeding at the rate of three miles in two hours ; and two hours afterwards met a stage waggon, which was moving at the rate of 9 miles in 4 hours.
Página 450 - If then we suppose the factors corresponding to the negative and imaginary roots to be already multiplied together, each factor x— a corresponding to a positive root introduces at least one change of sign ; therefore no equation can have more positive roots than it has changes of sign. To prove the second part of Descartes...
Página 109 - Pr always denotes the number of factors in the formula we are using. Ex. 1. Four persons enter a carriage in which there are six seats : in how many ways can they take their places ? The first person may seat himself in 6 ways ; and then the second person in 5 ; the third in 4 ; and the fourth in 3 ; and since each of these ways may be associated with each of the others, the required answer is б x 5 x 4 x 3, or 360.
Página 13 - Hence if any three terms of a proportion are given, the fourth may be found. Thus if...
Página 172 - The integral part of a logarithm is called the characteristic, and the decimal part is called the mantissa.
Página 482 - A railway train after travelling for one hour meets with an accident which delays it one hour, after which it proceeds at three-fifths of its former rate, and arrives at the terminus...
Página 455 - Every equation of an odd degree has at least one real root whose sign is opposite to that of its last term.