Algebra for Schools and CollegesLongmans, Green & Company, 1895 - 309 páginas |
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Página 247
... mean between two numbers equals 0 ; the geometrical mean equals V - 1 ; the harmonical mean equals co . What are the numbers ? CHAPTER XXXI . INDETERMINATE COEFFICIENTS . 355. Convergent and Divergent HARMONICAL PROGRESSION . 247.
... mean between two numbers equals 0 ; the geometrical mean equals V - 1 ; the harmonical mean equals co . What are the numbers ? CHAPTER XXXI . INDETERMINATE COEFFICIENTS . 355. Convergent and Divergent HARMONICAL PROGRESSION . 247.
Página 250
... convergent . That is , when a lies between 1 and 1 . 364. If the value of each term of a series , which is alternately positive and negative , is less than the preceding term , the series is convergent . For let the series be - V1 V2 V3 ...
... convergent . That is , when a lies between 1 and 1 . 364. If the value of each term of a series , which is alternately positive and negative , is less than the preceding term , the series is convergent . For let the series be - V1 V2 V3 ...
Página 263
... convergent series , we may assume that , ( 1 + x ) " = A + Bx + Ca2 + Da3 + .... Now , substituting for n , Р զ ( 1 + x ) = A + Bx + Cœ2 + Dæ3 + ... , which equals , when each member is raised to the 9th power , ( 1 + x ) 2 = ( A + Bæ ...
... convergent series , we may assume that , ( 1 + x ) " = A + Bx + Ca2 + Da3 + .... Now , substituting for n , Р զ ( 1 + x ) = A + Bx + Cœ2 + Dæ3 + ... , which equals , when each member is raised to the 9th power , ( 1 + x ) 2 = ( A + Bæ ...
Página 302
... convergent a1 + is called the second 1 1 convergent , a1 + a2 + so on . Let - a2 is called the third convergent , and be any fraction in its lowest terms . Divide a by b , and let a1 equal the 302 ALGEBRA .
... convergent a1 + is called the second 1 1 convergent , a1 + a2 + so on . Let - a2 is called the third convergent , and be any fraction in its lowest terms . Divide a by b , and let a1 equal the 302 ALGEBRA .
Página 305
... convergent , a1 , is too small because the part 1 1 A 2 + Az + ... U is omitted . The second convergent , a1 + denominator a , is CONTINUED FRACTIONS . 305.
... convergent , a1 , is too small because the part 1 1 A 2 + Az + ... U is omitted . The second convergent , a1 + denominator a , is CONTINUED FRACTIONS . 305.
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Algebra for Schools and Colleges (Classic Reprint) William Freeland Sin vista previa disponible - 2018 |
Términos y frases comunes
a²+2ab+b² a²b a²b² a²x a³b a³b² a³b³ ab+b² ab¹ ab² ab³ algebraic arithmetical ax² b²)² binomial factors Clearing of fractions coefficient common factor Complete divisor Completing the square continued fraction convergent cube root decimal divided divisor equal EXAMPLE EXERCISE exponent expression Extract the square Find the H. C. F. find the number form of x² formula given gives harmonical mean Hence integral last term least common Least Common Multiple letters logarithm mantissa minus mixed surd monomial Multiply numbers whose product numbers whose sum operation indicated parenthesis Perform the operation permutations polynomial positive integer quadratic equation quotient radical Reduce remainder result second terms Solve the following square root subtract Transpose and unite trinomial unknown quantities Va² x²y x²y² xy³
Pasajes populares
Página 20 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Página 21 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Página 217 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Página 271 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log
Página 220 - If three quantities are in continued proportion, the first is to the third as the square of the first is to the square of the second. Let a : b = b : c. Then, 2=*. b с Therefore, ^xb. = ^x± b с bb Or °r
Página 214 - In any proportion, the product of the means equals the product of the extremes.
Página 284 - For the first place can be filled in n ways, the second in n - 1 ways, the third place in n - 2 ways, and the rth place in n - (r - 1) ways.
Página 258 - If the coefficient of any term be multiplied by the exponent of a in that term, and the result divided by the exponent of x in the term increased by 1, the quotient will be the coefficient of the next following term.
Página 82 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.