F.5 Math geometric sequence(2)

2015-04-12 12:00 am

A boy draws some straight lines on a paper. Initially, he draws the first straight
line of length 2cm from a point A0 to a point A1. Then, starting from A1, he draws the
second straight line of length 4cm to a point A2, and so on. A0,A1,A2, ... may not be
collinear. suppose the length of the nth line is 2^n cm.

a) express the total length of the first k straight lines drawn in terms of k.
(ans. 2^(k+1) -2 cm)
b) if (k+1) straight lines are drawn, is it possible that the point A(k+1) and A0
overlap with each other? Explain.

I want to ask how to use the answer of (a) to solve (b).
Please help. Thank you!!

回答 (1)

[匿名]

2015-04-12 1:00 am

✔ 最佳答案

(b) No, it isn't possible.
Since the total length of the first k straight lines drawn is 2^(k+1) -2,
which is shorter than the (k+1)th straight line (2^(k+1)), no matter how
the first k straight lines are arranged, the distance between Point A k
and A0 must be shorter than 2^(k+1). Therefore, it is never possible
that the point A(k+1) and A0 overlap with each other.

參考: myself

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