Sum series

  • Thread starter Suy
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  • #1
Suy
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Homework Statement



[PLAIN]http://img651.imageshack.us/img651/2219/unledybi.jpg [Broken]
can someone teach me how to do it ?
answer is k=1/2,-7/17
thanks

Homework Equations





The Attempt at a Solution

 
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Answers and Replies

  • #2
[tex]\sum_{n=1}^∞(3-27k)k^{2n}=(3-27k)\sum_{n=1}^∞(k^2)^n=(3-27k)(\sum_{n=0}^∞(k^2)^n-1)=(3-27k)(\frac{1}{1-k^2}-1)[/tex]
assuming [itex]|k|<1[/itex]
[tex](3-27k)(\frac{1}{1-k^2}-1)=-7k[/tex]
Now multiply with [itex](1-k^2) [/itex] and use your favorite CAS program to get
[tex]-3(-1+9k)k=7(-1+k^2)[/tex]
Now solve for k
 

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