how to simplify this please?

👨🏻‍🏫 學術台數學

KrC

2008-10-25 1:48 am

P+PxR+PxR^2+PxR^3+...+ PxR^n

請問點樣簡化以上算式？

Thanks

回答 (3)

[匿名]

2008-10-25 5:13 am

✔ 最佳答案

Let x be P+P*R+P*R^2+P*R^3+...+ P*R^n

x = P+P*R+P*R^2+P*R^3+...+ P*R^n - (1)
x*R = P*R + P*R^2 + P*R^3 + P*R^n + P*R^(n+1) - (2)

(2) - (1)
x*R - x = P * R^(n+1) - P
x(R-1) = P[R^(n+1) - 1]
x = P[R^(n+1) - 1] / (R-1)

∴P+P*R+P*R^2+P*R^3+...+ P*R^n = P[R^(n+1) - 1] / (R-1)

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Patrick仔

2008-10-25 2:44 am

here is the solution:

圖片參考：http://img511.imageshack.us/img511/8785/dfhfhxv5.jpg

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用戶5569

2008-10-25 2:04 am

P+PxR+PxR^2+PxR^3+...+ PxR^n = PxR^(n-1)

參考: 自己(f.4)

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