Higher Algebra: A Sequel to Elementary Algebra for Schools |
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Page xv
... zero By taking x small enough , any term of the series a + a1x + a‚x2 + 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 ...
... zero By taking x small enough , any term of the series a + a1x + a‚x2 + 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 ...
Page 36
... means being inserted in each case . 24. If the sum of an A. P. is the same for p as for q terms , shew that its sum for p + q terms is zero . CHAPTER V. GEOMETRICAL PROGRESSION . 51. DEFINITION . Quantities are 36 HIGHER ALGEBRA .
... means being inserted in each case . 24. If the sum of an A. P. is the same for p as for q terms , shew that its sum for p + q terms is zero . CHAPTER V. GEOMETRICAL PROGRESSION . 51. DEFINITION . Quantities are 36 HIGHER ALGEBRA .
Page 57
... zero . In like manner any number other than ten may be taken as the radix of a scale of notation ; thus if 7 is the radix , a number expressed by 2453 represents 2 × 73 + 4 × 7o + 5 × 7 + 3 ; and in this scale no digit higher than 6 can ...
... zero . In like manner any number other than ten may be taken as the radix of a scale of notation ; thus if 7 is the radix , a number expressed by 2453 represents 2 × 73 + 4 × 7o + 5 × 7 + 3 ; and in this scale no digit higher than 6 can ...
Page 61
... zero . 81. To express a given radix fraction in any proposed scale . Let F be the given fraction , and r the radix of the proposed scale . Let b1 , b , b , ... be the required digits beginning from the left ; then b . b . F = 1 + + + γ ...
... zero . 81. To express a given radix fraction in any proposed scale . Let F be the given fraction , and r the radix of the proposed scale . Let b1 , b , b , ... be the required digits beginning from the left ; then b . b . F = 1 + + + γ ...
Page 75
... zero unless each of them is separately zero ; that is , a = 0 , and b = 0 . 99. If a + b - 1 = c + d - 1 , then a = c , and b = d . For , by transposition , ac + ( bd ) -1 = 0 ; therefore , by the last article , a - c = 0 , and b d = 0 ...
... zero unless each of them is separately zero ; that is , a = 0 , and b = 0 . 99. If a + b - 1 = c + d - 1 , then a = c , and b = d . For , by transposition , ac + ( bd ) -1 = 0 ; therefore , by the last article , a - c = 0 , and b d = 0 ...
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Other editions - View all
Higher Algebra: A Sequel to Elementary Algebra for Schools H. S. Hall,S. R. Knight No preview available - 2017 |
Higher Algebra: A Sequel to Elementary Algebra for Schools (Classic Reprint) H. S. Hall No preview available - 2017 |
Higher Algebra: A Sequel to Elementary Algebra for Schools H. S. Hall,S. R. Knight No preview available - 2018 |
Common terms and phrases
a+b+c+ a₁ Algebra annuity arithmetic mean arithmetical progression ascending powers ax² b₁ Binomial Theorem C₁ C₂ complete quotient compound interest continued fraction cube root denominator denote digits divisible Elementary Algebra equal equation x² Example expression factors Find the coefficient find the number Find the sum find the value finite geometrical progression given log given series greater greatest term hence infinite series less letters limit logarithms multiplying negative nth term number of solutions number of terms Ny² obtain orders of differences P₁ partial fractions positive integers preceding article proper fraction prove quadratic quadratic equation r+1)th term radix ratio rational integral function recurring series scale of relation series is convergent series is divergent shew solution in positive Solve suppose u₁ U₂ unity vergent whence zero
Popular passages
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Page 175 - The logarithm of a product is equal to the sum of the logarithms of its factors.
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Page 454 - 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...
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Page 367 - DEFINITION. If an event can happen in a ways and fail in b ways, and. each of these ways is equally likely, the probability, or the chance, of its happening is , and...
Page 492 - Geese, which were proceeding at the rate of 3 miles in 2 hours, he afterwards met a stage wagon, which was moving at the rate of 9 miles in 4 hours. B overtook the same drove of Geese at the 45th mile stone, and met the same stage wagon exactly forty minutes before he came to the 31st mile stone. Where was B when A reached London 1 Solution.
Page 178 - The integral part of a logarithm is called the characteristic, and the decimal part is called the mantissa.
Page 130 - There are n points in a plane, no three of which are in the same straight line with the exception of p, which are all in the same straight line; find the number of lines which result from joining them.
Page 486 - 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...