Challenging Mathematical Problems with Elementary Solutions, 第 1 卷Holden-Day, 1964 - 440 頁 |
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第 1 到 3 筆結果,共 29 筆
第 126 頁
... coefficient of x " is ( -1 ) m ( 0 for m = n ( compare with part b ) . - ( ) = 1 . ( " m1 ) for m < n and 57g . The sum to be evaluated equals the coefficient of x in the polynomial ( 1 + x ) " + ( 1 + x ) ” + 1 + ( 1 + x ) n + 2 + ...
... coefficient of x " is ( -1 ) m ( 0 for m = n ( compare with part b ) . - ( ) = 1 . ( " m1 ) for m < n and 57g . The sum to be evaluated equals the coefficient of x in the polynomial ( 1 + x ) " + ( 1 + x ) ” + 1 + ( 1 + x ) n + 2 + ...
第 127 頁
... coefficient of x2 " in the expression [ 1 - x2n + 1 ( 1 x2n + 1 ( 1 − x ) 2n + 1 ] 1 - - [ 1 − x2n + 1 ( 1 − x ) 2n + 1 ] x ) 2n + 171 + x 1 x + x2 1 + x3 By virtue of the ... coefficient of x V. Problems on the binomial coefficients 127.
... coefficient of x2 " in the expression [ 1 - x2n + 1 ( 1 x2n + 1 ( 1 − x ) 2n + 1 ] 1 - - [ 1 − x2n + 1 ( 1 − x ) 2n + 1 ] x ) 2n + 171 + x 1 x + x2 1 + x3 By virtue of the ... coefficient of x V. Problems on the binomial coefficients 127.
第 128 頁
... coefficient of x " in the expression 2n + 1 ( 1 + x ) " ( 1 + x + x2 + · · · ) − ( 1 + x ) 2n + 1 ( 1 + x + x2 + · · · ) = ... If we multiply any polynomial P ( x ) = a + a ̧x + a2x2 + ··· + aμXÑ by 1 + x + x2 + ... , then the ...
... coefficient of x " in the expression 2n + 1 ( 1 + x ) " ( 1 + x + x2 + · · · ) − ( 1 + x ) 2n + 1 ( 1 + x + x2 + · · · ) = ... If we multiply any polynomial P ( x ) = a + a ̧x + a2x2 + ··· + aμXÑ by 1 + x + x2 + ... , then the ...
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