maths sequence ....

👨🏻‍🏫 學術台數學

☆ 天與空 ★ ◤

2008-09-27 8:32 pm

(a) Find the sum of the first eight terms of the geometric progression
1/2 , -1/1/2 , 4/1/2 , ...
(b) If a is proportional to (b+c) and b is proportional to (c+a) , show that a is proportional to b.

p.s. solve (b) only !!
thanks

更新1:

-1/1/2 and 4/1/2 mean -1又1/2 and 4又1/2 respectively ~~ thanks

回答 (1)

用戶10012

2008-09-27 9:45 pm

✔ 最佳答案

(b)
a=k(b + c) where k is a constant.
a = kb + kc
c = (a-kb)/k...........(1)
b = h(c +a) where h is a constant.
b = hc + ha
c = (b-ah)/h............(2)
(1)=(2)
(a - kb)/k = ( b - ah)/h
ha - hkb = kb - hka
a(h + hk) = b(k + hk)
a = (k + hk)b/(h + hk)
therefore, a is proportional to b.

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maths sequence ....