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Side 280
... expansion of ( x + a ) " , and when we put this series in the place of ( x + a ) " we are said to expand ( x + a ) " . The theorem was discovered by Newton . 505. For example , take ( x + a ) ; here n = 5 , n ( n - 1 ) 5.4 = 10 , n ( n ...
... expansion of ( x + a ) " , and when we put this series in the place of ( x + a ) " we are said to expand ( x + a ) " . The theorem was discovered by Newton . 505. For example , take ( x + a ) ; here n = 5 , n ( n - 1 ) 5.4 = 10 , n ( n ...
Side 281
... expansion of ( x + a ) " suppose x = 1 ; thus , ( 1 + a ) " = 1 + na + n ( n − 1 ) 1.2 - a2 + n ( n − 1 ) ( n − 2 ) 1.2.3 - a3 + ...... + a " ; since this is true whatever a may be , we may write x for a ; thus , ( 1 + x ) * = 1 + nt ...
... expansion of ( x + a ) " suppose x = 1 ; thus , ( 1 + a ) " = 1 + na + n ( n − 1 ) 1.2 - a2 + n ( n − 1 ) ( n − 2 ) 1.2.3 - a3 + ...... + a " ; since this is true whatever a may be , we may write x for a ; thus , ( 1 + x ) * = 1 + nt ...
Side 282
... expansion of ( x + a ) " . The 7th term of the expansion is n ( n − 1 ) ... ... ( n − r + 2 ) xn − r + 1 r 1 x2 - r + 1 α - 1 ; the ( r + 1 ) th term may be obtained by multiplying the 7th by n - r + 1 ጽ • α - X α that is , by ( " + ...
... expansion of ( x + a ) " . The 7th term of the expansion is n ( n − 1 ) ... ... ( n − r + 2 ) xn − r + 1 r 1 x2 - r + 1 α - 1 ; the ( r + 1 ) th term may be obtained by multiplying the 7th by n - r + 1 ጽ • α - X α that is , by ( " + ...
Side 283
... expansion is equal to the ( p + 1 ) th term , and these terms are greater than any other term ; but if n + 1 Ꮳ α + 1 be not an integer , then the greatest term is the ( +1 ) th where q is the integral part of n + 1 · х + 1 a 511. In ...
... expansion is equal to the ( p + 1 ) th term , and these terms are greater than any other term ; but if n + 1 Ꮳ α + 1 be not an integer , then the greatest term is the ( +1 ) th where q is the integral part of n + 1 · х + 1 a 511. In ...
Side 283
... expansion of ( x + a ) " , and when we put this series in the place of ( x + a ) " we are said to expand ( x + a ) " . The theorem was discovered by Newton . 505. For example , take ( x + a ) 3 ; here n = = 5 , thus , n ( n - 1 ) 5.4 ...
... expansion of ( x + a ) " , and when we put this series in the place of ( x + a ) " we are said to expand ( x + a ) " . The theorem was discovered by Newton . 505. For example , take ( x + a ) 3 ; here n = = 5 , thus , n ( n - 1 ) 5.4 ...
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7th term a+b+c arithmetic mean arithmetical ax² Binomial Theorem black balls chance cloth coefficient common contains continued fraction convergent Crown 8vo denote digits divided divisible divisor equal event example expansion Extract the square factors Fcap Find the number Geometrical Progression greater than unity Hence least common multiple less than unity letters logarithm miles multiply negative quantity number of combinations number of terms obtain occur P₁ positive integers positive quantity preceding article prime number probability problem quadratic equation quadratic surd quotient radix ratio recurring decimal remainder result scale shew shillings Similarly solution square number square root subtraction suppose supposition surd things taken trial unknown quantities white balls whole number
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