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(1 +ｘ) 2ｎ=( 1 +ｘ) ｎ( 1 +ｘ) ｎ 是一个恒等式 ,利用ｘｎ 的系数对应相等 ,我们可以证明 (Ｃ0ｎ) 2 +(Ｃ1ｎ) 2 +(Ｃ2 ｎ) 2 +… +(Ｃｎｎ) 2 =Ｃｎ2ｎ这一个论证方法是继二项式定理中“赋值法”求组合数代数和后 ,能够用来解决另一类组合数运算的一个有效方法 .此法可归
(1 + x) 2n = ( 1 + x) n ( 1 + x) n is an identity. Using the coefficients of xn for correspondence, we can prove (C0n) 2 + (C1n) 2 + (C2 n) 2 +... +(Cnn) 2 =Cn2n This method of argument is an effective method that can be used to solve another type of combinatorial number operation after the “assignment method” in binomial theorem to find the algebraic sum of combinatorial numbers.