Elements of Algebra with ExercisesMacmillan Company, 1902 - 478 páginas |
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Página xiv
... PROGRESSIONS . § 1 . SERIES § 2. ARITHMETICAL PROGRESSION 379 379 Arithmetical Means 384 Problems 386 § 3. GEOMETRICAL PROGRESSION 389 Sum of an Infinite Geometrical Progression 393 Geometrical Means 394 Problems 395 · § 4. HARMONICAL ...
... PROGRESSIONS . § 1 . SERIES § 2. ARITHMETICAL PROGRESSION 379 379 Arithmetical Means 384 Problems 386 § 3. GEOMETRICAL PROGRESSION 389 Sum of an Infinite Geometrical Progression 393 Geometrical Means 394 Problems 395 · § 4. HARMONICAL ...
Página 378
... = 0 . -- 29. 5 x3 - 3x2 - 14 = 0 . 22. 2- % + 52-1-11 = 0 24. 5x - 2x2 - 16 – 0 . 26. 5 x ̄ − 2 x ̄ ‡ – 3 − 0 . - = 28. 7x - 3x 4 = 0 . - - 30. 2x + 5x - 7 = 0 . CHAPTER XXVII . PROGRESSIONS . § 1 . 1. A 378 [ CH . XXVI ALGEBRA .
... = 0 . -- 29. 5 x3 - 3x2 - 14 = 0 . 22. 2- % + 52-1-11 = 0 24. 5x - 2x2 - 16 – 0 . 26. 5 x ̄ − 2 x ̄ ‡ – 3 − 0 . - = 28. 7x - 3x 4 = 0 . - - 30. 2x + 5x - 7 = 0 . CHAPTER XXVII . PROGRESSIONS . § 1 . 1. A 378 [ CH . XXVI ALGEBRA .
Página 379
... 1. An Arithmetical Series , or as it is more commonly called an Arithmetical Progression ( A. P. ) , is a series in which each term , after the first , is formed by adding 379 CHAPTER XXVII PROGRESSIONS § 1 SERIES ARITHMETICAL PROGRESSION.
... 1. An Arithmetical Series , or as it is more commonly called an Arithmetical Progression ( A. P. ) , is a series in which each term , after the first , is formed by adding 379 CHAPTER XXVII PROGRESSIONS § 1 SERIES ARITHMETICAL PROGRESSION.
Página 380
... progression . 3. The common difference may be either positive or negative . If d be positive , each term is greater than the preceding , and the series is called a rising , or an increasing progression . E.g. , 1+ 2+ 3 + 4 + ...
... progression . 3. The common difference may be either positive or negative . If d be positive , each term is greater than the preceding , and the series is called a rising , or an increasing progression . E.g. , 1+ 2+ 3 + 4 + ...
Página 381
... progression , the sum of n terms is equal to one - half the product of the number of terms and the sum of the first and the nth term , i.e. , Sn = 2 ( a1 + an ) . ( II . ) Since the successive terms in an arithmetical progression , from ...
... progression , the sum of n terms is equal to one - half the product of the number of terms and the sum of the first and the nth term , i.e. , Sn = 2 ( a1 + an ) . ( II . ) Since the successive terms in an arithmetical progression , from ...
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Elements of Algebra with Exercises George Egbert Fisher,Isaac Joachim Schwatt Sin vista previa disponible - 2016 |
Términos y frases comunes
a₁ a²b a²b² a²x a²x² a³b ab² absolute value algebraic language ALGEBRAIC NUMBERS arithmetical arithmetical means assigned number ax² binomial coefficient Commutative Law complex number continued fraction convergent cube definition denominator digits divided divisor dollars equal number equivalent exactly divisible example illustrates EXERCISES exponent Find the values following expressions following principle given equation greater illustrates the following imaginary unit inequality integer irrational number less Let x stand logarithm miles minuend monomial multinomial multiplied negative numbers obtained parentheses positive integer positive number positive units powers quadratic equation quadratic surds r₁ radicand rational number remainder required numbers result second member Simplify solution Solve the equation square root summands symbolically unknown number whence wherein x²y xy² yards
Pasajes populares
Página 209 - Nos. 1 and 2, 3 and 4, 5 and 6, 7 and 8, 9 and 10, 11 and 12.
Página 356 - IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth...
Página 73 - Divide the first term of the dividend by the first term of the divisor, the result will be the first term of the quotient.
Página 414 - C„.r. That is, the number of combinations of n dissimilar .things r at a time is equal to the number of combinations of the n things n — r at a time.
Página 359 - In any proportion the terms are in proportion by Composition and Division; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Página 326 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel, in going 120 yards; but if the circumference of each wheel...
Página 166 - The product of two fractions is a fraction whose numerator is the product of the numerators of the given fractions, and whose denominator is the product of the given denominators.
Página 472 - We therefore have : (i.) The characteristic of the logarithm of a number greater than unity is positive, and is one less than the number of digits in its integral part.
Página 418 - Thus, 16 x2, ± -^/(a? — ж2), etc., are functions of x; corresponding to any value of x, the first function has one value, the second has two values. Again, the area of a circle is a function of its radius ; the distance a train runs is a function of the time and speed. 4. Much simplicity is introduced into mathematical investigations by employing special symbols for functions. The symbol f(x), read function of x, is very commonly used to denote a function of x.
Página 363 - One quantity is said to vary directly as a second and inversely as a third, when it varies as the second and the reciprocal of the third jointly.