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 19 筆
第 15 頁
... BINOMIAL COEFFICIENTS The following problems will illustrate certain properties of the numbers = n ! k ! ( n − k ) ! • n ( n − 1 ) ( n − k + 1 ) ... binomial theorem to evaluate the following sums V. Problems on the binomial coefficients 15.
... BINOMIAL COEFFICIENTS The following problems will illustrate certain properties of the numbers = n ! k ! ( n − k ) ! • n ( n − 1 ) ( n − k + 1 ) ... binomial theorem to evaluate the following sums V. Problems on the binomial coefficients 15.
第 18 頁
... binomial theorem to evaluate the following sums : n a . b . n n + + ( ) ( ) + ( 1 ) ( x ) + ( 2 ) ( km2 ) + m m + 1 ... binomial coefficients it is sometimes n k is the number of combinations of n helpful to make use of the fact that ...
... binomial theorem to evaluate the following sums : n a . b . n n + + ( ) ( ) + ( 1 ) ( x ) + ( 2 ) ( km2 ) + m m + 1 ... binomial coefficients it is sometimes n k is the number of combinations of n helpful to make use of the fact that ...
第 164 頁
... binomial coefficients . Just as this formula can be used to construct Pascal's triangle , equation ( 2 ) can be used to construct a table of the numbers The above calculation of H is needed to start the process . We obtain the array 1 1 ...
... binomial coefficients . Just as this formula can be used to construct Pascal's triangle , equation ( 2 ) can be used to construct a table of the numbers The above calculation of H is needed to start the process . We obtain the array 1 1 ...
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A₁ A₂ An+m arrangements b₁ b₂ binomial coefficients binomial theorem bishops black squares C₁ chessboard chord circle coefficient color column compute the number Consequently consider corresponding customers denote determine the number diagonals digits dihedral angle divided divisible draw equally likely possible equation equidistant equivalence classes exactly example experiment favorable outcomes follows formula G₁ given Hence inclusion and exclusion intersection k-gons knights length mathematical induction maximum number n-gon number of different number of favorable number of paths number of shortest obtain pairs partition passengers plane points A1 polygons positive integers possible outcomes Pr{E probability theory problem 54 prove queens rectangle relatively prime remaining required probability rooks segment selected at random sequence shortest paths side solution to problem solved sphere square controlled Suppose total number triangle unfavorable values vertex vertices