Prove that 3^(n-1)(nC1)+3^(n-2)(nC2)+...+3(nCn-1)+nCn=4^(n-1)+4^(n-2)(3)+...+4(3^n-2)+3^n-1.
更新1:
點解4^n-3^n=(4-3)(.................)?
Pure Maths Binomial Theorem
2007-11-03 9:30 pm
Let n be a positive integer greater than 1.By considering the expansion of (1+x)^n,
Prove that 3^(n-1)(nC1)+3^(n-2)(nC2)+...+3(nCn-1)+nCn=4^(n-1)+4^(n-2)(3)+...+4(3^n-2)+3^n-1.
Prove that 3^(n-1)(nC1)+3^(n-2)(nC2)+...+3(nCn-1)+nCn=4^(n-1)+4^(n-2)(3)+...+4(3^n-2)+3^n-1.
回答 (1)
2007-11-03 9:49 pm
✔ 最佳答案
As follows~~~圖片參考：http://i182.photobucket.com/albums/x4/A_Hepburn_1990/puremaths.jpg?t=1194068940
2007-11-03 14:06:09 補充：
For this, you may refer to the chapter polynomial.a^n - b^n = (a - b)(a^n-1 + a^n-2 b + ... + ab^n-2 + b^n-1)This is an identity.
參考: Myself~~~
收錄日期: 2021-04-26 18:36:57
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