A Treatise on AlgebraHarper & Brothers, 1868 - 384 páginas |
Dentro del libro
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Página 235
... series when the number of terms is infinite , divide the first term by unity diminished by the ratio . The sum of the terms of a decreasing series may be repre- sented by the formula S = a - rl 1 - r Now , in a decreasing series , each ...
... series when the number of terms is infinite , divide the first term by unity diminished by the ratio . The sum of the terms of a decreasing series may be repre- sented by the formula S = a - rl 1 - r Now , in a decreasing series , each ...
Página 237
... series 1 , 2 , 4 , 8 , 16 , etc. S = арт α r - 1 -214-1-16383 , Ans . 4. Find the sum of 12 terms of the series 1 ... infinite progression whose first term is 1 , and the sum of the series . Ans . 1 . 16. Find the first term of an ...
... series 1 , 2 , 4 , 8 , 16 , etc. S = арт α r - 1 -214-1-16383 , Ans . 4. Find the sum of 12 terms of the series 1 ... infinite progression whose first term is 1 , and the sum of the series . Ans . 1 . 16. Find the first term of an ...
Página 265
... series by dividing the numerator by the denominator , ac- cording to the usual method of division . 1 Ex . 1. Expand into an infinite series . 1 - x ) 1 1 - x 1 - x 4 ... infinite SERIES . 265 Development of Algebraic Expressions into Series.
... series by dividing the numerator by the denominator , ac- cording to the usual method of division . 1 Ex . 1. Expand into an infinite series . 1 - x ) 1 1 - x 1 - x 4 ... infinite SERIES . 265 Development of Algebraic Expressions into Series.
Página 266
Elias Loomis. 1 + x Ex . 5. Convert into an infinite series . 1 - x а + x Ex . 6. Convert into an infinite series . a- XC 2x 2x2 2x3 2x4 Ans . 1+ + + + a2 a3 Ex . 7. Convert 1 1 − x + x2 1 - x Ex . 8. Convert 1 - x + x2 1 + x α into an ...
Elias Loomis. 1 + x Ex . 5. Convert into an infinite series . 1 - x а + x Ex . 6. Convert into an infinite series . a- XC 2x 2x2 2x3 2x4 Ans . 1+ + + + a2 a3 Ex . 7. Convert 1 1 − x + x2 1 - x Ex . 8. Convert 1 - x + x2 1 + x α into an ...
Página 267
... infinite series . X x2 Ans . a + + X3 5x4 2a 8a3 16a5—128a7 + , etc. 4 Ex . 3. Develop the square root of a1 + x into an infinite series . Ex . 4. Develop the square root of a * -x into an infinite series . Ex . 5. Develop the square ...
... infinite series . X x2 Ans . a + + X3 5x4 2a 8a3 16a5—128a7 + , etc. 4 Ex . 3. Develop the square root of a1 + x into an infinite series . Ex . 4. Develop the square root of a * -x into an infinite series . Ex . 5. Develop the square ...
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Términos y frases comunes
algebraic arithmetical progression binomial binomial theorem cent coefficient common denominator common difference compound interest continued fraction cube root decimal denote digits Divide the number dividend divisible dollars equa equal equation whose roots EXAMPLES exponent expression Extract the square factors figure Find the cube Find the fifth Find the fourth Find the number Find the square Find the sum find the values following RULE fourth power geometrical progression Given greatest common divisor Hence indicates infinite series last term least common multiple less logarithm miles monomial Multiply negative nth root number of terms obtain polynomial positive preceding Prob problem quotient radical sign ratio real roots Reduce remainder represent Resolve result second degree second term Solve the equation square root Sturm's Theorem subtract suppose surd third tion unity unknown quantity whence whole number zero
Pasajes populares
Página 72 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Página 141 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Página 39 - ... the square of the second. In the second case, (ab)2 = a?-2ab + bi. (2) That is, the square of the difference of two numbers 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 54 - Divide the less number by the remainder, the last divisor by the last remainder, and so on, till nothing remains. The last divisor will be the greatest common divisor sought.
Página 46 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Página 181 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left. How much wine did he draw each time ? 50.
Página 227 - In arithmetical progression there are five parts to be considered, viz : the first term, the last term, the number of terms, the common difference, and the sum of all the terms.
Página 204 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Página 220 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Página 202 - A , where m=c 9. Find two numbers such that their sum, their product, and the difference of their squares may be all equal to one another.