Higher Algebra: A Sequel to Elementary Algebra for SchoolsMacmillan, 1891 - 557 páginas |
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Página xiii
... n is a positive integer General term of the expansion The expansion may be made to depend upon the case in which the first term is unity . Second proof of the binomial theorem The coefficients of terms equidistant from the beginning and ...
... n is a positive integer General term of the expansion The expansion may be made to depend upon the case in which the first term is unity . Second proof of the binomial theorem The coefficients of terms equidistant from the beginning and ...
Página 28
... term of the series from that which follows it . In the first of the above examples the common difference is 4 ; in ... nth term , we have l = a + ( n − 1 ) d . 40. To find the sum of a number of terms in Arithmetical Progression . Let a ...
... term of the series from that which follows it . In the first of the above examples the common difference is 4 ; in ... nth term , we have l = a + ( n − 1 ) d . 40. To find the sum of a number of terms in Arithmetical Progression . Let a ...
Página 29
... n terms = n ( a + 1 ) , n . * . 8 = ( a + 1 ) .... 2 l = a + ( n − 1 ) d ....... n - - .. 8 = { 2a + ( n − 1 ) d } ... term of a series is 5 , the last 45 , and the sum 400 : find the number of terms , and the common difference . If n ...
... n terms = n ( a + 1 ) , n . * . 8 = ( a + 1 ) .... 2 l = a + ( n − 1 ) d ....... n - - .. 8 = { 2a + ( n − 1 ) d } ... term of a series is 5 , the last 45 , and the sum 400 : find the number of terms , and the common difference . If n ...
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... terms of the series whose nth term is 3n - 1 . By putting n = 1 , and n = p respectively , we obtain first term = 2 , last term = 3p - 1 ; ... sum = 2 ( 2 + 3p − 1 ) = ( 3p + 1 ) . - EXAMPLES . IV . a . 1. Sum 2 , 3 , 4 , ... to 20 terms ...
... terms of the series whose nth term is 3n - 1 . By putting n = 1 , and n = p respectively , we obtain first term = 2 , last term = 3p - 1 ; ... sum = 2 ( 2 + 3p − 1 ) = ( 3p + 1 ) . - EXAMPLES . IV . a . 1. Sum 2 , 3 , 4 , ... to 20 terms ...
Página 32
... term is 2 , the last term 29 , the sum 155 ; find the difference . 19. The sum of 15 terms of an A. P. is 600 , and ... nth term is 4n + 1 . 24. Find the sum of 35 terms of the series whose pth term is + 2 . 7 n 25. Find the sum of p ...
... term is 2 , the last term 29 , the sum 155 ; find the difference . 19. The sum of 15 terms of an A. P. is 600 , and ... nth term is 4n + 1 . 24. Find the sum of 35 terms of the series whose pth term is + 2 . 7 n 25. Find the sum of p ...
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Otras ediciones - Ver todas
Higher Algebra: A Sequel to Elementary Algebra for Schools H. S. Hall,S. R. Knight Sin vista previa disponible - 2017 |
Higher Algebra: A Sequel to Elementary Algebra for Schools (Classic Reprint) H. S. Hall Sin vista previa disponible - 2017 |
Higher Algebra: A Sequel to Elementary Algebra for Schools H. S. Hall,S. R. Knight Sin vista previa disponible - 2018 |
Términos y frases comunes
a+b+c a₁ Algebra annuity arithmetic mean arithmetical progression ax² b₁ balls Binomial Theorem C₁ C₂ CAMB COLL common difference common ratio complete quotient contains continued fraction decimal denominator denote digits divided divisible equal event Example expansion expression factors find the chance find the number Find the sum find the value finite geometric Geometrical Progression given series greater harmonic means hence In+1 infinite series less letters logarithms multiplying negative nth term number of shot number of solutions number of terms obtain P₁ partial fractions positive integers preceding article prime number proper fraction prove quadratic quadratic equation quantities radix recurring decimal result scale of relation series is convergent shew shillings Similarly Solve the equations suppose U₁ U₂ unity varies whence zero
Pasajes populares
Página 55 - ... any number divided by 9 will leave the same remainder as the sum of its digits divided by 9.
Página 169 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Página 111 - The number of combinations of n things г at a time is equal to the number of combinations of n things n—r at a time.
Página 488 - At the 50th mile stone from London, A overtook a drove of geese which were proceeding at the rate of three miles in two hours ; and two hours afterwards met a stage waggon, which was moving at the rate of 9 miles in 4 hours.
Página 450 - If then we suppose the factors corresponding to the negative and imaginary roots to be already multiplied together, each factor x— a corresponding to a positive root introduces at least one change of sign ; therefore no equation can have more positive roots than it has changes of sign. To prove the second part of Descartes...
Página 109 - Pr always denotes the number of factors in the formula we are using. Ex. 1. Four persons enter a carriage in which there are six seats : in how many ways can they take their places ? The first person may seat himself in 6 ways ; and then the second person in 5 ; the third in 4 ; and the fourth in 3 ; and since each of these ways may be associated with each of the others, the required answer is б x 5 x 4 x 3, or 360.
Página 13 - Hence if any three terms of a proportion are given, the fourth may be found. Thus if...
Página 172 - The integral part of a logarithm is called the characteristic, and the decimal part is called the mantissa.
Página 482 - A railway train after travelling for one hour meets with an accident which delays it one hour, after which it proceeds at three-fifths of its former rate, and arrives at the terminus...
Página 455 - Every equation of an odd degree has at least one real root whose sign is opposite to that of its last term.