Elementary Algebra |
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Page 351
... convergent when the sum of the first n terms cannot numerically exceed some finite quantity however great n may be ... convergent or divergent by examining whether the series remains finite , or becomes in- finite , when n is made ...
... convergent when the sum of the first n terms cannot numerically exceed some finite quantity however great n may be ... convergent or divergent by examining whether the series remains finite , or becomes in- finite , when n is made ...
Page 352
... convergent . finite limit 1 1 - x If x is numerically greater than 1 , the sum of the first n terms is 21 , and by taking n sufficiently great , this can be X- made greater than any finite quantity ; thus the series is divergent . If x ...
... convergent . finite limit 1 1 - x If x is numerically greater than 1 , the sum of the first n terms is 21 , and by taking n sufficiently great , this can be X- made greater than any finite quantity ; thus the series is divergent . If x ...
Page 353
... convergent it will remain convergent , and if 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 ...
... convergent it will remain convergent , and if 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 ...
Page 354
... convergent series in which the terms may increase up to a certain point and then begin to 99 100 ' decrease . For ... convergent . [ Art . 445. ] If λ > 1 , the series is divergent . [ Art . 447. ] If λ = 1 , the series may be either ...
... convergent series in which the terms may increase up to a certain point and then begin to 99 100 ' decrease . For ... convergent . [ Art . 445. ] If λ > 1 , the series is divergent . [ Art . 447. ] If λ = 1 , the series may be either ...
Page 355
... convergent or divergent ? Ип n2xn - 1 Here Lim = = Lim = x . Un - 1 ( n − 1 ) 2xn− 2 Hence if x < 1 the series is convergent ; if x1 the series is divergent . If x 1 the series becomes 12 + 22 + 32 + 42 + ... , and is obviously ...
... convergent or divergent ? Ип n2xn - 1 Here Lim = = Lim = x . Un - 1 ( n − 1 ) 2xn− 2 Hence if x < 1 the series is convergent ; if x1 the series is divergent . If x 1 the series becomes 12 + 22 + 32 + 42 + ... , and is obviously ...
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Common terms and phrases
a+3b a+b+c a₁ a²+b² arithmetic means arithmetical arranged ascending powers b₁ beginner Binomial Theorem cents CHAPTER coefficients column compound expression continued fraction convergent cube root decimal denote digits dimes Divide dividend division divisor equal EXAMPLES XI Find the highest find the number Find the square Find the sum find the value following expressions given expressions greater harmonic mean Hence highest common factor integer less letters logarithm lowest common multiple method miles an hour Multiply number of terms numerator and denominator obtain partial fractions prefixed prove quadratic quadratic equation quotient ratio remainder Resolve into factors result rule of signs second term Simplify SIMULTANEOUS EQUATIONS solution square root subtraction Suppose surds symbols Transposing unknown quantity walk whence write yards zero
Popular passages
Page 331 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 256 - In a quadratic equation wJiere the coefficient of the first term is unity, (i) the sum of the roots is equal to the coefficient of x with its sign changed ; (ii) the product of the roots is equal to the third term.
Page 168 - Thus the 4th root (2x2) = the square root of the square root ; the sixth root (3x2) = the cube root of the square root, or the square root of the cube root.
Page 178 - A basket of oranges is emptied by one person taking half of them and one more, a second person taking half of the remainder and one more, and a third person taking half of the remainder and six more. How many did the basket contain at first ? 17.
Page 179 - Two vessels contain mixtures of wine and water ; in one there is three times as much wine as water, in the other five times as much water as wine. Find how much must be drawn off from each to fill a third vessel which holds seven gallons, in order that its contents may be half wine and half water.
Page 280 - The pressure of wind on a plane surface varies jointly as the area of the surface, and the square of the wind's velocity. The pressure on a square foot is 1...
Page 213 - Art. 167 we saw that if the number of unknown quantities is greater than the number of independent equations, there will be an unlimited number of solutions, and the equations will be indeterminate. By introducing conditions, however, we can limit the number of solutions. When positive integral values of the unknown quantities are required, the equations are called simple indeterminate equations. The introduction of this restriction enables us to express the solutions in a very simple form. Ex. 1....