數學m2,求救,binomial theorem
2011-02-22 6:08 am
(A) it is given that k=Pk(k-1)-Qk(k+1),find the values of P and Q(B)using the results of (A),show that the summation of k as i goes from 1 to n=1/2n(n+1)A part 可以唔使計，，要B part既full step!!!求
回答 (1)
2011-02-22 7:21 am
✔ 最佳答案
(A)Pk(k-1) - Qk(k+1)= Pk² - Pk - Qk² - Qk
= (P-Q)k² - (P+Q)k
So P - Q = 0 and P + Q = - 1
P = Q = - 1/2
B)n
Σ k
k = 1
=
n
Σ = (-1/2)k(k-1) - (-1/2)k(k+1)
k = 1
=
n
Σ = (1/2)k(k+1) - (1/2)k(k-1)
k = 1
=
{n - 1 ................}...............................n
{ Σ = (1/2)k(k+1) } +(1/2)n(n+1) - .....Σ = (1/2)(k-1)k
{k = 1................}.............................k=1
= (1/2)n(n+1)
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