Higher Algebra: A Sequel to Elementary Algebra for SchoolsMacmillan, 1891 - 557 páginas |
Dentro del libro
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Página xi
... unity ; 1 + w + w2 = 0 . Powers of w · Examples VIII . b . PAGE 2313 62 68 • 64 65 67 68 69 70 72 74 75 75 75 77 77 79 79 គ 8 80 81 CHAPTER IX . THE THEORY OF QUADRATIC EQUATIONS . A quadratic equation cannot have more than two roots ...
... unity ; 1 + w + w2 = 0 . Powers of w · Examples VIII . b . PAGE 2313 62 68 • 64 65 67 68 69 70 72 74 75 75 75 77 77 79 79 គ 8 80 81 CHAPTER IX . THE THEORY OF QUADRATIC EQUATIONS . A quadratic equation cannot have more than two roots ...
Página xiii
... unity . Second proof of the binomial theorem The coefficients of terms equidistant from the beginning and end are equal . Sum of the coefficients . . 137 139 140 141 142 • • 143 143 146 Sum of coefficients of odd terms is equal to sum ...
... unity . Second proof of the binomial theorem The coefficients of terms equidistant from the beginning and end are equal . Sum of the coefficients . . 137 139 140 141 142 • • 143 143 146 Sum of coefficients of odd terms is equal to sum ...
Página xxi
... unity Linear factors of a3 + b3 + c3 - 3abc Value of a + b + cn when a + b + c = 0 Examples XXXIV . b . • Elimination . Elimination by symmetrical functions Euler's method of elimination Sylvester's Dialytic Method · Bezout's method ...
... unity Linear factors of a3 + b3 + c3 - 3abc Value of a + b + cn when a + b + c = 0 Examples XXXIV . b . • Elimination . Elimination by symmetrical functions Euler's method of elimination Sylvester's Dialytic Method · Bezout's method ...
Página 35
... ; the sum of these means exceeds their number by unity : how many means are there ? 8. The sum of n terms of the series 2 , 5 , 8 , ... is 950 : find n . 1 9 . Sum the series 1 1 + √x 3-2 ARITHMETICAL PROGRESSION . 35 Examples IV.
... ; the sum of these means exceeds their number by unity : how many means are there ? 8. The sum of n terms of the series 2 , 5 , 8 , ... is 950 : find n . 1 9 . Sum the series 1 1 + √x 3-2 ARITHMETICAL PROGRESSION . 35 Examples IV.
Página 46
... unity . 21. If S , denote the sum of n terms of a G. P. whose first term is a , and common ratio r , find the sum of S1 , S3 , S5 , ... S2n - 1 . 22. If S1 , S2 , S3 , ... S , are the sums of infinite geometric series , whose first ...
... unity . 21. If S , denote the sum of n terms of a G. P. whose first term is a , and common ratio r , find the sum of S1 , S3 , S5 , ... S2n - 1 . 22. If S1 , S2 , S3 , ... S , are the sums of infinite geometric series , whose first ...
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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.