Higher Algebra: A Sequel to Elementary Algebra for SchoolsMacmillan, 1891 - 557 páginas |
Dentro del libro
Resultados 1-5 de 37
Página xvii
... successive convergents Pn¶n - 1 - Pn - 19n = ( − 1 ) n . Examples XXV . a . • • 275 276 277 278 The convergents gradually approximate to the continued fraction . Limits of the error in taking any convergent for the continued fraction ...
... successive convergents Pn¶n - 1 - Pn - 19n = ( − 1 ) n . Examples XXV . a . • • 275 276 277 278 The convergents gradually approximate to the continued fraction . Limits of the error in taking any convergent for the continued fraction ...
Página xix
... successive convergents • by b2 a1 + a2 + has a definite value if Lim ... anan + 10 . bntl b1 by а1 - a2- ... The convergents to are positive proper fractions in ascend- ing order of magnitude , if an 1 + bn General value of convergent ...
... successive convergents • by b2 a1 + a2 + has a definite value if Lim ... anan + 10 . bntl b1 by а1 - a2- ... The convergents to are positive proper fractions in ascend- ing order of magnitude , if an 1 + bn General value of convergent ...
Página 27
... successive days there were respectively 6 , 5 and 3 races . Which days were these , and how long did the regatta last ? 19. The price of a diamond varies as the square of its weight . Three rings of equal weight , each composed of a ...
... successive days there were respectively 6 , 5 and 3 races . Which days were these , and how long did the regatta last ? 19. The price of a diamond varies as the square of its weight . Three rings of equal weight , each composed of a ...
Página 58
... successive powers of the radix are no longer powers of ten , in determining the carrying figures we must not divide by ten , but by the radix of the scale in question . Example 1. In the scale of eight subtract 371532 from 530225 , and ...
... successive powers of the radix are no longer powers of ten , in determining the carrying figures we must not divide by ten , but by the radix of the scale in question . Example 1. In the scale of eight subtract 371532 from 530225 , and ...
Página 60
... successive divisions by the radix of the proposed scale . Example 1. Express the denary number 5213 in the scale of seven . 7 ) 5213 7 ) 744 ...... 5 7 ) 106 ...... 2 7 ) 15 ...... 1 2 ...... 1 Thus 5213 = 2 × 74 + 1 × 73 + 1 × 72 + 2 ...
... successive divisions by the radix of the proposed scale . Example 1. Express the denary number 5213 in the scale of seven . 7 ) 5213 7 ) 744 ...... 5 7 ) 106 ...... 2 7 ) 15 ...... 1 2 ...... 1 Thus 5213 = 2 × 74 + 1 × 73 + 1 × 72 + 2 ...
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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.