The elements of algebra1857 |
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Σελίδα 185
... 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 187
... expansion of ( x + a ) " . The 1st term is x " , 2nd ...... na1x ” -1 , 2-1 3rd n . a'x " - " , ..... 4th n . " ...... 2 n - 1 n - 2 3 a3x " -3 , in which we observe that the coefficient of any term is formed of the pro- n n - 1 n - 2 ...
... expansion of ( x + a ) " . The 1st term is x " , 2nd ...... na1x ” -1 , 2-1 3rd n . a'x " - " , ..... 4th n . " ...... 2 n - 1 n - 2 3 a3x " -3 , in which we observe that the coefficient of any term is formed of the pro- n n - 1 n - 2 ...
Σελίδα 188
... expansion may be found independently of the rest . Ex . Required the fifth term of ( a2— b2 ) 13 . Here r = 5 , and n = 12 ; 12.11.10.9 .. term required = ( −6 * ) ! . ( a * ) " , 1.2.3.4 = 495a1o68 . 316. If the index of the binomial ...
... expansion may be found independently of the rest . Ex . Required the fifth term of ( a2— b2 ) 13 . Here r = 5 , and n = 12 ; 12.11.10.9 .. term required = ( −6 * ) ! . ( a * ) " , 1.2.3.4 = 495a1o68 . 316. If the index of the binomial ...
Σελίδα 189
... 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 190
... expansion of ( 3 + 5x ) , when x = - 1 2 • Here ( n + 1 ) . b a + b 518 2 = ( 8 + 1 ) . = 9x = 5 45 11 11 411 . The first whole number greater than 4 is 5 ; therefore the term required is the 5th . 320. To find the sum of all the ...
... expansion of ( 3 + 5x ) , when x = - 1 2 • Here ( n + 1 ) . b a + b 518 2 = ( 8 + 1 ) . = 9x = 5 45 11 11 411 . The first whole number greater than 4 is 5 ; therefore the term required is the 5th . 320. To find the sum of all the ...
Συχνά εμφανιζόμενοι όροι και φράσεις
algebraical quantities annuity Arithmetical Progression Binomial Theorem coefficient common denominator Comp contain continued fraction convergent cube root denary difference digits divided divisible divisor Edition equal equation EXERCISES expressed Extract the square factors Find the G.C.M. find the number Find the square find the sum Find the value given greater Greatest Common Measure Hence hour latter Least Common Multiple less lowest terms miles Mult multiplied N₁ negative nth root number of combinations number of terms numerator and denominator positive integers Post 8vo Present Value prime number proportion proposed quantities prove quadratic quadratic equation quotient radix ratio reduced remainder represented rule scale shew shillings square root ST JOHN'S COLLEGE subtracted suppose surd unknown quantities vols vulgar fraction whole number Woodcuts
Δημοφιλή αποσπάσματα
Σελίδα 574 - Ephemera. — The Book of the Salmon: Comprising the Theory, Principles, and Practice of Fly-fishing for Salmon: Lists of good Salmon Flies for every good River in the Empire ; the Natural History of the Salmon, all its known Habits described, and the best way of artificially Breeding it explained. With numerous coloured Engravings. By EPHEMERA j assisted by ANDREW YOUNG.
Σελίδα 577 - Kirby and Spence's Introduction to Entomology ; or, Elements of the Natural History of Insects : Comprising an Account of Noxious and Useful Insects, of their Metamorphoses, Food, Stratagems, Habitations, Societies, Motions, Noises, Hybernation, Instinct, &c.