SOLUTION: Consider {{{ ( sqrt(n) + sqrt(n-1)) ( sqrt(n) - sqrt(n-1)) }}} =1 for n >or= 1 -Provide two numerical examples illustrating validity. -Show the statement is true in general.

Algebra ->  Finance -> SOLUTION: Consider {{{ ( sqrt(n) + sqrt(n-1)) ( sqrt(n) - sqrt(n-1)) }}} =1 for n >or= 1 -Provide two numerical examples illustrating validity. -Show the statement is true in general.       Log On


   

Question 957377: Consider +%28+sqrt%28n%29+%2B+sqrt%28n-1%29%29+%28+sqrt%28n%29+-+sqrt%28n-1%29%29+ =1 for n >or= 1
-Provide two numerical examples illustrating validity.
-Show the statement is true in general.
-What is the difference between using numerical values to show that something is true and showing in general that something is true?
Thank you for any help you may provide!
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Consider +%28+sqrt%28n%29+%2B+sqrt%28n-1%29%29+%28+sqrt%28n%29+-+sqrt%28n-1%29%29+ =1 for n+%3Eor=+1
-Provide two numerical examples illustrating validity.
Let n = 1

%22%22=%22%221

%281%29%281%29-%281%29sqrt%280%29-sqrt%280%29sqrt%281%29%2Bsqrt%280%29sqrt%280%29%22%22=%22%221

1-%281%29%280%29%2B%280%29%281%29-%280%29%280%29%22%22=%22%221
 
1-0%2B0-0%22%22=%22%221

1%22%22=%22%221

----------------------

Let n = 2

%22%22=%22%221

2-sqrt%282%29sqrt%281%29-sqrt%281%29sqrt%282%29%2Bsqrt%281%29sqrt%281%29%22%22=%22%221

2-sqrt%282%29%281%29%2B%281%29sqrt%282%29-%281%29%281%29%22%22=%22%221
 
2-sqrt%282%29%2Bsqrt%282%29-1%22%22=%22%221

2-cross%28sqrt%282%29%29%2Bcross%28sqrt%282%29%29-1%22%22=%22%221

2-1%22%22=%22%221

1%22%22=%22%221

--------------------

-Show the statement is true in general. 
+%28+sqrt%28n%29+%2B+sqrt%28n-1%29%29+%28+sqrt%28n%29+-+sqrt%28n-1%29%29+%22%22=%22%221

Use FOIL:

%22%22=%22%221

%22%22=%22%221

sqrt%28n%29sqrt%28n%29-sqrt%28n-1%29sqrt%28n-1%29%22%22=%22%221

n-%28n-1%29%22%22=%22%221

n-n%2B1%22%22=%22%221

1%22%22=%22%221

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-What is the difference between using numerical values to show that
something is true and showing in general that something is true?
-When we use numerical values to show that something is true, we show it
ONLY for those particular numerical values and no others.

-What we show in general that something is true, we show it for all the
values stated, in this case for n+%3E=+1 

--------------------
Edwin