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Common terms and phrases
1)st term a₁ arithmetical means arithmetical progression assigned positive number b₁ c₁ b₂ C₂ Binomial Theorem common difference coördinates cubic equation d₁ d₂ decimal places degree denominator denote determinant digits divergent divisible equal EXAMPLE EXERCISES expansion factor Find the chance Find the sum finite formula function geometrical progression given graph harmonical means Hence increases without bound indeterminate form infinite series law of indices left member less than unity limit logarithms loge m₁ mathematical induction Multiplying negative nth term number of permutations number of terms obtain odd numbers P₁ partial fractions positive integer power series prove quadratic equation quantities quartic equation quotient rational number real numbers relation result roots series is convergent Similarly simultaneous equations Solve square symbol u₁ u₂ vanishes y₁ zero
Popular passages
Page 63 - Find the area of a circle whose radius is 12 feet, from the law that the area of a circle varies as the square of its radius.
Page 71 - June, 1889.) 1. In how many years will a sum of money double itself at 4 per cent., interest being compounded semi-annually ? 2.
Page 18 - I. The logarithm of a product equals the sum of the logarithms of the factors.
Page 204 - Thus ike modulus of the product of two complex numbers is the product of their moduli, and the argument of the product is the sum of their arguments.
Page 65 - Geometrical Progression. A series of quantities is said to be in geometrical progression when the ratio of each term...
Page 180 - The sum of the products of the roots taken two at a time is equal to the coefficient of the third term.
Page 60 - In any proportion, the product of the extremes equals the product of the means.
Page 117 - An infinite series is convergent, if from and after any fixed term the ratio of each term to the preceding term is numerically less than some quantity which is itself numerically less than unity.
Page 65 - The sum of 2n terms of a geometrical progression, whose first term is a and common ratio r...
Page 73 - A rational integral function of the n'h degree in x cannot vanish for more than n values of x, unless the coefficients of all the powers of x are zero. For, if / (ж) , being of the form ax" + bxn~l + cx"~2 H , vanish for the n values a, ß, у ..., it must be equivalent to a(xu)(x-ß)(xy)—.