The elements of algebra1857 |
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Page 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 ...
Page 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 ...
Page 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 ...
Page 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 ...
Page 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 ...
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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
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