compared to 2 questions:
1:
S(n): 1^2 +2^2 +...(2n)^2 = 1/3(n)(2n+1)(4n+1)
2:
S(n): 1^3+3^3+...(2n-1)^3 = n^2(2n^2-1)
In the first question, why when sub n=1, LHS = 1^2 + 2^2??However, in the second question, LHS is just equal to 1^3. Why? What is the principle?
F.4 amaths - M.I concept
2006-11-02 4:55 am
回答 (1)
2006-11-02 5:15 am
✔ 最佳答案
因為此 n 不同彼ｎ．n=1 不一定是第一個term. 要看清楚．
First consider LHS.
let f(n)=1^2 + 2^2 + ..+(2n)^2
Do you know what is f(1) ?
it is
f(1)=1^2 + ... 加到去 ...+2(1)^2
= 1^2 + 2^2
f(2)=1^2 + 2^2 + 3^2 + 4^2
f(n)=1^2 + 2^2 + ..+(2n)^2
RHS.
g(n)=(n)(2n+1)(4n+1) / 3
g(1)=3
therefore n=1, f(1)=g(1).
2. Same way to think.
let f(n)=LHS
f(n)= 1^3+3^3+...+(2n-1)^3
f(1)=1^3 +... 加到去 ...+ ( 2(1)-1 ) ^3
=1^3
其他我諗你識做．
收錄日期: 2021-04-12 22:40:44
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20061101000051KK04024