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Old 2005-08-21, 05:22   #1
DSC
 
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Default help with math

I have this problem but can't solve it! Can some one help??

Derive this expression interm of n

"Summation (i*3^i); this summation is from i =1 to n "

my prof. give a hint that multiply out side and inside the summation
[1/(3-1)]*Summation[i*3^3 * (3-1)].

thanks for your looking!!!
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Old 2005-08-21, 07:11   #2
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Mathematica gives the answer:

3/4 * (1 - 3^n + 2*3^n)

You should be able to verify that using induction.
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Old 2005-08-21, 10:43   #3
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After your prof's hint, try to see if it looks like a derivative.

It's a homework problem so would appreciate it if folks limited it to hints and did not give away answers.
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Old 2005-08-21, 11:15   #4
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You can do it without derivatives. Use your Prof's hint, split the sum into two sums, substitute the variable of summation in one sum suitably so both sums contain like powers of 3, join the two sums again and simplify.

Alex
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Old 2005-08-22, 02:24   #5
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thanks alotz.....but jinydu, would you tell me how did you get 3/4 * (1 - 3^n + 2*3^n)......i've been trying to figure it out, but i couldn't find the answer anywayz :(
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Old 2005-08-22, 03:50   #6
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Quote:
Originally Posted by DSC
thanks alotz.....but jinydu, would you tell me how did you get 3/4 * (1 - 3^n + 2*3^n)......i've been trying to figure it out, but i couldn't find the answer anywayz :(
I used a computer program...

Admittedly, garo's and akruppa's solutions are better, since they don't involve this kind of "cheating".

Last fiddled with by jinydu on 2005-08-22 at 03:51
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Old 2005-08-30, 02:40   #7
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I don’t understand why I look into a mirror, and then a dimple in the right side of my face turns to opposite side. Could you explain why it is?
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Old 2005-08-30, 03:14   #8
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Quote:
Originally Posted by DSC
I don’t understand why I look into a mirror, and then a dimple in the right side of my face turns to opposite side. Could you explain why it is?
The Law of Reflection...

Last fiddled with by jinydu on 2005-08-30 at 03:14
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Old 2005-08-30, 17:55   #9
ewmayer
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Jinydu, you probably just gravely offended the adherents of some major religion which doesn't believe in the law of reflection. I think we need to overhaul science curricula worldwide to expose students to this still-simmering scientific controversy. (Hey, if even one person in the whole world doesn't believe it, it is by definition controversial.)
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Old 2005-08-30, 17:58   #10
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Quote:
Originally Posted by ewmayer
Jinydu, you probably just gravely offended the adherents of some major religion which doesn't believe in the law of reflection. I think we need to overhaul science curricula worldwide to expose students to this still-simmering scientific controversy. (Hey, if even one person in the whole world doesn't believe it, it is by definition controversial.)
Yeah!

Why mirrors swap left and right, but don't swap up with down?

Luigi
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Old 2005-08-30, 21:10   #11
xilman
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Quote:
Originally Posted by ET_
Yeah!

Why mirrors swap left and right, but don't swap up with down?

Luigi
They swap neither. They swap front and back.

Paul
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