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Help with a C1 level question

  • Thread starter CathyLou
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Show that http://www.artofproblemsolving.com/Forum/latexrender/pictures/4cb05ba8a17dcb9e2dcfb9ef1a98966a.gif [Broken] where k is a constant to be found.

I know that a = 2 and that d = 1/2 and substituting these figires into Sn = (2a + (n-1) d) gives n/2 (4 + (n-1)/2) but I just can't see how to get from n/2 (4 + (n-1)/2) to the answer of 1/4n(n+7). I'd really appreciate it if someone could please explain.

Thank you.

Cathy
 
Last edited by a moderator:

AlephZero

Science Advisor
Homework Helper
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Try using

4 + (n-1)/2 = (8+n-1)/2 = (n+7)/2
 
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Try using

4 + (n-1)/2 = (8+n-1)/2 = (n+7)/2
Thanks for replying but I still don't understand how you get from 4 + (n-1)/2 to (8+n-1)/2.
 

cristo

Staff Emeritus
Science Advisor
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Thanks for replying but I still don't understand how you get from 4 + (n-1)/2 to (8+n-1)/2.
In order to put 4 over the denominator 2, you must first multiply it by 2. Let's consider a general example: [tex] \frac{a}{b}+\frac{c}{d}=\frac{ad+cb}{bd} [/tex]

Now applying this to your case we have, strictly speaking, [tex]\frac{4}{1}+\frac{n-1}{2}=\frac{2(4)+1(n-1)}{2}=\frac{8+n-1}{2} [/tex]
 
Last edited:
173
0
In order to put 4 over the denominator 2, you must first multiply it by 2. Let's consider a general example: [tex] \frac{a}{b}+\frac{c}{d}=\frac{ad+cb}{bd} [/tex]

Now applying this to your case we have, strictly speaking, [tex]\frac{4}{1}+\frac{n-1}{2}=\frac{2(4)+1(n-1)}{2}=\frac{8+n-1}{2} [/tex]
Thanks for your help.

I understand it now.

Cathy
 

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