The elements of algebraParker, 1845 - 287 σελίδες |
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Σελίδα 173
... expansion will be of n dimensions , n being the index of the power to which the binomial is raised . Also , if each term of the proposed binomial be of two dimensions , every term in the expansion will be of 2n dimensions ; and so on ...
... expansion will be of n dimensions , n being the index of the power to which the binomial is raised . Also , if each term of the proposed binomial be of two dimensions , every term in the expansion will be of 2n dimensions ; and so on ...
Σελίδα 175
... expansion of ( x + a ) " . The 1st term is x " , 2nd ......... 3rd 4th na1x2 - 1 , n - 1 n . a2x2 - 2 , 2 n - n . 1 n 2 a3x - 3 2 3 in which we observe that the coefficient of any term is formed of the pro- duct of the factors n n- - 1 ...
... expansion of ( x + a ) " . The 1st term is x " , 2nd ......... 3rd 4th na1x2 - 1 , n - 1 n . a2x2 - 2 , 2 n - n . 1 n 2 a3x - 3 2 3 in which we observe that the coefficient of any term is formed of the pro- duct of the factors n n- - 1 ...
Σελίδα 176
... expansion , formed from the index , is a positive integer . For the coefficient of the ( r + 1 ) th term is n ( n − 1 ) ( n − 2 ) ... ( n − r + 1 ) ; − 1 2 • 3 ........ − r and this ( by Art . 301 ) is the same as the number of ...
... expansion , formed from the index , is a positive integer . For the coefficient of the ( r + 1 ) th term is n ( n − 1 ) ( n − 2 ) ... ( n − r + 1 ) ; − 1 2 • 3 ........ − r and this ( by Art . 301 ) is the same as the number of ...
Σελίδα 177
... expansion of ( x + a ) " , so as to deduce that of ( a + x ) " , and then equating the coefficients of similar terms in the two expansions , which are clearly equal to each other . COR . Hence in expanding a binomial , with the index a ...
... expansion of ( x + a ) " , so as to deduce that of ( a + x ) " , and then equating the coefficients of similar terms in the two expansions , which are clearly equal to each other . COR . Hence in expanding a binomial , with the index a ...
Σελίδα 178
... expansion of ( 3 + 5x ) , when x = 1 Here ( n + 1 ) b a + b = ( 8 + 1 ) . = 9x 5 45 - 11 11 572 = 2 4 . The first whole number greater than 4 is 5 ; therefore the term required is the 5th . 320. To find the sum of all the coefficients ...
... expansion of ( 3 + 5x ) , when x = 1 Here ( n + 1 ) b a + b = ( 8 + 1 ) . = 9x 5 45 - 11 11 572 = 2 4 . The first whole number greater than 4 is 5 ; therefore the term required is the 5th . 320. To find the sum of all the coefficients ...
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a+b+c a²x² algebraical quantities annuity Arithmetical Progression Binomial Theorem coefficient common denominator compound interest continued fraction cube root difference digits divided divisible divisor equal equation expressed extracting the square factors Find the G. C. M. find the number Find the square Find the value given greater Greatest Common Measure Hence Least Common Multiple less lowest terms Mult multiplied negative number of combinations number of terms numerator and denominator positive integers Present Value prime number probability proposed quantity prove quadratic quadratic equation quotient ratio reduced remainder represent rule shew shillings square root subtracted supposition surd unknown quantities vulgar fraction whole number
Δημοφιλή αποσπάσματα
Σελίδα 286 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 139 - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Σελίδα 77 - Divide this quantity, omitting the last figure, by twice the part of the root already found, and annex the result to the root and also to the divisor, then multiply the divisor as it now stands by the part of the root last obtained for the subtrahend.
Σελίδα 107 - A laborer agreed to serve for 36 days on condition that for every day he worked he should receive $1.25, and for every day he was absent he should forfeit 50 cents.
Σελίδα 4 - RULE. Multiply all the numerators together for a new numerator, and all the denominators for a new denominator: then reduce the new fraction to its lowest terms.
Σελίδα 132 - Ratio is the relation which one quantity bears to another in respect of magnitude, the comparison being made by considering what multiple, part, or parts, one is of the other.
Σελίδα civ - The hold of a vessel partly full of water (which is uniformly increased by a leak) is furnished with two pumps worked by A and B, of whom A takes three strokes to two of .B's ; but four of .B's throw out as much water as five of A's. Now...
Σελίδα 31 - The sign of equality, called equal, or equal to, signifies that the quantities between which it is placed are equal to each other.
Σελίδα 112 - This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQUARE.
Σελίδα 3 - If the numerator and denominator of a fraction be multiplied by the same number, the value of the fraction is not altered.