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9. Find the coefficient of x lO in the power series of each of
these functions.
a. (x^2 +x^4 +x^6 +x^8 + .. . )(x^3 +x^6 +x^9 + .. ·)(x^4 +
x^8 +X^12 + ... )
b. (I +x^2+x^4+x^6+ x^8+ ... )(1 +x^4+X^8+X^I2 + ... )
(I +x^6 +x^12 +x^18 + ... )
asked in Mathematical Logic by Veteran (23.9k points)
retagged by | 167 views

For last it is 500 combination ...may be help you 

We need to manually count here all the combinations ,am i correct?Like the way you have written
yes we have to calculate coeffient of x^10 so we make x^10 by given x terms ..
bro is there a straightway shortcut by which you written 1 for all 5 cases or you calculated using binomial formula?
see first i wrote 1+x^2+x^4... =1/1-x^2 , which is sum of infinite gp ..

then i used 1/(1-x)^n = n-1+rcr x^r , here x= x^2 , r vary according to coefficient ....
Thanks so much Sir, for your reply and the formula. May you please tell me from where you got this formula/?

rosen chapter 6 , .. you will get all open and closed form of generating function ... for more clearification 

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