A Treatise on Algebra: By Charles Smith |
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Page xiii
... convergent series • 320 321-323 323 325 326 If Za „ x2 = 2b , x2 , for all values of x for which the series are con- vergent , then ar = b , Examples XXVI . • CHAPTER XXII . THE BINOMIAL THEOREM . ANY INDEX . Proof of the theorem 329 ...
... convergent series • 320 321-323 323 325 326 If Za „ x2 = 2b , x2 , for all values of x for which the series are con- vergent , then ar = b , Examples XXVI . • CHAPTER XXII . THE BINOMIAL THEOREM . ANY INDEX . Proof of the theorem 329 ...
Page xiv
... convergent or both divergent . 420 1 Σκη convergent or divergent according as the limit of n xiv CONTENTS .
... convergent or both divergent . 420 1 Σκη convergent or divergent according as the limit of n xiv CONTENTS .
Page xv
... convergent 452 Convergency of continued fractions . 455 Periodic continued fractions 453 • Reduction of quadratic surds to continued fractions Series expressed as continued fractions Examples XXXVII . . 460 . 465 468 CHAPTER XXVIII ...
... convergent 452 Convergency of continued fractions . 455 Periodic continued fractions 453 • Reduction of quadratic surds to continued fractions Series expressed as continued fractions Examples XXXVII . . 460 . 465 468 CHAPTER XXVIII ...
Page 312
... convergent , and S is called its sum . Thus 1 + 1 + 1 + } + ... .. is a convergent series whose sum is 2 . When the sum of the first n terms of a series increases numerically without limit as n is increased indefinitely , the series is ...
... convergent , and S is called its sum . Thus 1 + 1 + 1 + } + ... .. is a convergent series whose sum is 2 . When the sum of the first n terms of a series increases numerically without limit as n is increased indefinitely , the series is ...
Page 313
... convergent nor divergent . Such a series is some- times called an indeterminate or a neutral series * . For example , the series 1-1 + 1-1 + ... is an indeter- minate series , for the sum of n terms is 1 or 0 according as n is odd or ...
... convergent nor divergent . Such a series is some- times called an indeterminate or a neutral series * . For example , the series 1-1 + 1-1 + ... is an indeter- minate series , for the sum of n terms is 1 or 0 according as n is odd or ...
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Common terms and phrases
a+b+c a₁ arithmetic mean arithmetical progression ax² b₁ binomial Binomial Theorem C₁ Cambridge coefficient contain continued fraction Crown 8vo denominator determinant digits divergent divide divisible divisor Edition equal equation ax example expansion Extra fcap Fcap Find the number Find the sum follows geometrical progression given expression Globe 8vo greater Hence the required infinity letters logarithm MACMILLAN'S Multiply negative nth convergent nth root nth term number of terms obtained P₁ periodic continued fraction positive integer powers prime number Professor prove quadratic equation quadratic surd quotient ratio remainder School Shew Solve the equation square root subtract suppose Theorem Trinity College u₁ unknown quantities white ball whole number zero
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