中四附加數學

hi! ivan 啱啱做完呢題
let S(n) to be the statement "[n(n-1)+1]+[n(n-1)+3]+......+[n(n-1)+(2n-1)] = n^3"
when n =1 ,
LHS= 1
RHS = 1
.'.S(n) is true.
Assume S(k) is true . i.e."[k(k-1)+1]+[k(k-1)+3]+......+[k(k-1)+(2k-1)] = k^3"
When n=k+1
LHS = [k(k+1)+1]+[k(k+1)+3]+......+[k(k+1)+(2k-1)] +[k(k+1)+(2k+1)]
= k^3 +[k(k+1)+(2k+1)] +2k(k)
= k^3+2k^2+k^2+k+2k +1
=(k+1)^3
=RHS
.'.S(k) is true .
By mathematical induction , S(n) is true for all natural no. n

2007-09-13 22:10:26 補充：
.'.S(k 1) is true .

2007-09-13 22:10:42 補充：
十