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有位中学里的朋友,给我写来一封信,综合他的意思有三点,第一点,二项式定理的系数表倒底是巴斯葛发见的,还是中国人呢?第二点,可否从系数表里導出二项式定理?第三点,二项式定理除了用数学歸纳法组合理论证明外是否还有证明?我想也许有些朋友有同样的想法,因此,我写成这篇文字公开地答复这些问题,可能有许多错误,愿意和大家讨论讨论。 (一)中国人首先创造了二项式定理系数表在中国古舊的书堆里,我们找得一件宝贝——开多乘方法。由于长期封建制度的摧残,得不到继续的发展,到了开拓出来的时候已是快要绝跡了。我们
One of my friends in the middle school wrote me a letter. There are three points in his synthesis. The first point is that the coefficient table of the Binomial Theorem was found by Pascal, or is it Chinese? Point, can you derive the binomial theorem from the coefficient table? The third point, the binomial theorem in addition to the theory of mathematical induction combined to prove whether there is proof? I think maybe some friends have the same idea, so I wrote this Texts openly answer these questions. There may be many mistakes and they are willing to discuss and discuss with others. (a) The Chinese first created the Binomial Theorem Coefficient Table in the ancient book pile in China, and we found a baby-open multiplication method. Due to the destruction of the long-term feudal system, no further development can be achieved, and it is almost time for it to be developed. we