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在高中课本中有这样一道习题:证明:C_n~1+2C_n~2+3C_n~3…+nC_u~n=n·2~(n-1)。本文给出它的七种不同的证明方法,这些证法从不同的侧面代表了数列求和的一般途径,对同学们或许有所启发。
In high school textbooks there is such an exercise: Proof: C_n~1+2C_n~2+3C_n~3...+nC_u~n=n·2~(n-1). This article gives its seven different methods of proof, which represent the general way of summation of numbers from different sides and may be inspiring to the students.