數學題—指數

7^(n-1)(7^3-1)/[2X7X7^(n-1)]
=342/14
=171/7

2007-09-07 15:31:32 補充：
TAKE COMMON FACTOR 7^(n-1) from both 分子 and 分母DO THE SIMPLE SIMPLIFICATION.YOU CAN FIND THE ANSWER

2007-09-07 17:19:54 補充：
FIRST,7^(n 1)=7^(n-1)X7 YOU MUST HAVE TO KNOW!!7^(n 2)=7^(n-1)X7^27^(n-1)(7^3-1)/[2X7X7^(n-1)]Since 7^3-1=342, 2X7=14SO 342/14COMMON FACTOR7^(n-1) can be cancelled out

2007-09-07 17:22:29 補充：
IF YOU STILL DO NOT UNDERSTAND, YOU CAN SEND A E-MAIL TO ME,

7^( n+2 ) -7^( n-1)
--------------------------
2 ．7^n

= [ ( 7^n x 7^2 ) - ( 7^n x 7^-1 ) ] / [2 x 7^n] <-----抽出7^n (by law of indices)*

= [ 7^2 - 7^-1 ] / 2 <----- 上下約掉7^n

= 171 / 7


*解釋
7^( n + 2 ) = 7^n x 7^2

7^( n - 1 ) = 7^n x 7^-1

其實是怎樣約掉7^n呢？詳細如下：

[ ( 7^n x 7^2 ) - ( 7^n x 7^-1 ) ] / [2 x 7^n]

= [ 7^n (7^2 - 7^-1) ] / [ 7^n ( 2 ) ] <------------ 上面抽出common factor 7^n

= [ 7^2 - 7^-1 ] / 2



其實，遇見這類題目應先看看分子與分母有什麼類似之處，

然後想辦法把相同之處抽出來，並約掉來簡化計算。

有時要盡量把index弄到一樣，就有可能約掉一些東西。

例如是：

{ 2x[7^(n+1)] - 2[7^(n+2)] } / (x - 7)

= { 2x[7^(n+1)] - 2.7[7^(n+1)]} / (x - 7)

= 7^(n+1)(2x - 14) / (x - 7) <----------觀察2x-14與x-7的關係

= 2 . 7^(n+1)(x - 7) / (x - 7)

= 2 . 7^(n+1)

我想你要寫清楚條題目:

7^( n+2 ) -7^( n-1)
--------------------------
2 ．7^n

個答案係：

= 7^( n+2 ) / (2．7^n) - 7^( n-1 ) / (2．7^n)

= ( 7^2 ) / 2 - 1 / ( 2．7 )

= 171 / 7

仲有無深一點的題目要問?

7^(n-1)(7^3-1)/[2X7X7^(n-1)]
=342/14
=171/7

7^(n+2) - 7^(n-1)
--------------------------
2 * 7^(n)

=

7^(3) * 7^(n-1) - 7^(n-1)
--------------------------------------
7^(n-1) * 2 * 7

=

7^(n-1) [7^(3) - 1]
------------------------------------
7^(n-1) *2 * 7

=

343 - 1
-------------------
14

=

171 / 7
================

oK^^? 1st one~~=333=

2007-09-07 15:36:27 補充：
/廿\發現得太慢添... 不過都比我啦~~

(7^n+2-7^n-1)/(2x7^n)
=(7^n x 7^2 - 7^n x 7^-1)/(2x7^n)
=7^n(49 - 1/7) / (2x7^n) 抽公因子7^n
=(49 - 1/7) / 2 約簡公因子7^n
=(342/7) / 2
=171 / 7

你個答案（171/7）點得來！？
請回答我！我學過

2007-09-07 15:39:35 補充：
[7^(n+2)-7^(n-1)]÷(2‧7^n)=(7^n×7-7^n÷7)÷(2×7^n)=[7^n(7-1/7)]÷(2×7^n)=48/7÷2=24/7

圖片參考：http://f20.yahoofs.com/hkblog/4TIncBOTHhmPSeRVWbHla4I-_1/blog/ap_20070907032023997.jpg?ibAez4GBr_CyoJVW

7^(n-1)(7^3-1)/[2X7X7^(n-1)]
=342/14
=171/7