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+1
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avatar+3994 

isn't the answer x divided by 2.

\(\frac{x^2+2x^4+3x^6+...+1005x^{2010}}{2x+4x^3+6x^5+...+2010x^{2009}}\)Simplify  

 

Pretty nice question. Try to see the pattern!

 Dec 22, 2018
edited by tertre  Dec 23, 2018
 #1
avatar+4424 
+2

\(\dfrac{\sum \limits_{k=1}^{1005}~k x^{2k}}{\sum \limits_{j=1}^{1005}~2jx^{2j-1}}=\\ \dfrac{x}{2}\dfrac{\sum \limits_{k=1}^{1005}~2k x^{2k}}{\sum \limits_{j=1}^{1005}~2jx^{2j}}=\\ \dfrac x 2\)

.
 Dec 22, 2018

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