Higher Algebra: A Sequel to Elementary Algebra for Schools |
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Page 153
... divergent , and we can only assert that if we multiply the series denoted by f ( m ) by the series denoted by ƒ ( n ) , the first r terms of the product will agree with the first r terms of ƒ ( m + n ) , whatever finite value may have ...
... divergent , and we can only assert that if we multiply the series denoted by f ( m ) by the series denoted by ƒ ( n ) , the first r terms of the product will agree with the first r terms of ƒ ( m + n ) , whatever finite value may have ...
Page 229
... divergent when the sum of the first n terms can be made numerically greater than any finite quantity by taking n sufficiently great . 278. If we can find the sum of the first n terms of a given series , we may ascertain whether it is ...
... divergent when the sum of the first n terms can be made numerically greater than any finite quantity by taking n sufficiently great . 278. If we can find the sum of the first n terms of a given series , we may ascertain whether it is ...
Page 230
... divergent . If x = 1 , the sum of the first n terms is n , and therefore the series is divergent . If x = 1 , the series becomes 1 − 1 + 1 − 1 + 1 − 1 + The sum of an even number of terms is 0 , while the sum of an odd number of ...
... divergent . If x = 1 , the sum of the first n terms is n , and therefore the series is divergent . If x = 1 , the series becomes 1 − 1 + 1 − 1 + 1 − 1 + The sum of an even number of terms is 0 , while the sum of an odd number of ...
Page 231
... divergent it will remain divergent , when we add or remove any finite number of its terms ; for the sum of these terms is a finite quantity . II . If a series in which all the terms are positive is con- vergent , then the series is ...
... divergent it will remain divergent , when we add or remove any finite number of its terms ; for the sum of these terms is a finite quantity . II . If a series in which all the terms are positive is con- vergent , then the series is ...
Page 233
... divergent . If the ratio is greater than unity , each of the terms after the fixed term is greater than u1 , and the sum of n terms is greater than nu ,; hence the series is divergent . 287. In the practical application of these tests ...
... divergent . If the ratio is greater than unity , each of the terms after the fixed term is greater than u1 , and the sum of n terms is greater than nu ,; hence the series is divergent . 287. In the practical application of these tests ...
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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
Page 61 - ... any number divided by 9 will leave the same remainder as the sum of its digits divided by 9.
Page 175 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 117 - 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.
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...
Page 11 - In any proportion the product of the extremes is equal to the product of the means. Let the proportion be a : b = с : d.
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...